{"id":35266,"date":"2023-01-08T12:03:14","date_gmt":"2023-01-08T06:33:14","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=35266"},"modified":"2023-01-08T00:03:33","modified_gmt":"2023-01-07T18:33:33","slug":"big-ideas-math-algebra-1-answers-chapter-9","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/big-ideas-math-algebra-1-answers-chapter-9\/","title":{"rendered":"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations"},"content":{"rendered":"<p>View <strong>Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations <\/strong>with step-by-step explanations from here. Students who are unable to solve quadratic equations can make use of our <em><a href=\"https:\/\/ccssanswers.com\/big-ideas-math-algebra-1-answers\/\">BIM Algebra 1 Answer Key<\/a><\/em> Ch 9 Solving Quadratic Equation. Download BIM Algebra 1 Solutions Key of Ch 9 Solving Quadratic Equations for free in order to prepare for the exams. BIM Algebra 1 Answer Key for Chapter 9 Solving Quadratic Equations Big Ideas Math Algebra 1 Answer Key includes resources like Questions from Exercises 9.1 to 9.6, Chapter Tests, Practice Tests, Cumulative Assessments, Review Tests, and so on.<\/p>\n<h2 class=\"entry-title\">Big Ideas Math Book Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations<\/h2>\n<p>Get hints, answers, and examples of <strong>BIM Algebra 1 Chapter 9 Solving Quadratic Equations <\/strong>from here. You will find Big Ideas Math Book Algebra 1 Answer Key Ch 9 Solving Quadratic Equation direct links in the below section. Learn different methods to solve quadratic equations here. You can access all the links easily and kickstart your preparation online or offline.<\/p>\n<ul>\n<li><a href=\"#Solving_Quadratic_Equations_Maintaining_Mathematical_Proficiency\">Solving Quadratic Equations Maintaining Mathematical Proficiency &#8211; Page 477<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Mathematical_Practices\">Solving Quadratic Equations Mathematical Practices &#8211; Page 478<\/a><\/li>\n<li><a href=\"#Lesson_9.1_Properties_of_Radicals\">Lesson 9.1 Properties of Radicals &#8211; Page(480-488)<\/a><\/li>\n<li><a href=\"#Properties_of_Radicals_9.1_Exercises\">Properties of Radicals 9.1 Exercises &#8211; Page(485-488)<\/a><\/li>\n<li><a href=\"#Lesson_9.2_Solving_Quadratic_Equations_by_Graphing\">Lesson 9.2 Solving Quadratic Equations by Graphing &#8211; Page(490-496)<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_by_Graphing_9.2_Exercises\">Solving Quadratic Equations by Graphing 9.2 Exercises &#8211; Page(494-496)<\/a><\/li>\n<li><a href=\"#Lesson_9.3_Solving_Quadratic_Equations_Using_Square_Roots\">Lesson 9.3 Solving Quadratic Equations Using Square Roots &#8211; Page(498-502)<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Using_Square_Roots_9.3_Exercises\">Solving Quadratic Equations Using Square Roots 9.3 Exercises &#8211; Page(501-502)<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Study_Skills:_Keeping_a_Positive_Attitude\">Solving Quadratic Equations Study Skills: Keeping a Positive Attitude &#8211; Page 503<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_9.1_\u2013_9.3_Quiz\">Solving Quadratic Equations 9.1 \u2013 9.3 Quiz &#8211; Page 504<\/a><\/li>\n<li><a href=\"#Lesson_9.4_Solving_Quadratic_Equations_by_Completing_the_Square\">Lesson 9.4 Solving Quadratic Equations by Completing the Square &#8211; Page(506-514)<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_by_Completing_the_Square_9.4_Exercises\">Solving Quadratic Equations by Completing the Square 9.4 Exercises &#8211; Page(511-514)<\/a><\/li>\n<li><a href=\"#Lesson_9.5_Solving_Quadratic_Equations_Using_the_Quadratic_Formula\">Lesson 9.5 Solving Quadratic Equations Using the Quadratic Formula &#8211; Page(516-524)<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Using_the_Quadratic_Formula_9.5_Exercises\">Solving Quadratic Equations Using the Quadratic Formula 9.5 Exercises &#8211; Page(521-524)<\/a><\/li>\n<li><a href=\"#Lesson_9.6_Solving_Nonlinear_Systems_of_Equations\">Lesson 9.6 Solving Nonlinear Systems of Equations &#8211; Page(526-532)<\/a><\/li>\n<li><a href=\"#Solving_Nonlinear_Systems_of_Equations_9.6_Exercises\">Solving Nonlinear Systems of Equations 9.6 Exercises &#8211; Page(530-532)<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Performance_Task:_Form_Matters\">Solving Quadratic Equations Performance Task: Form Matters &#8211; Page 533<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Chapter_Review\">Solving Quadratic Equations Chapter Review &#8211; Page(534-536)<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Chapter_Test\">Solving Quadratic Equations Chapter Test &#8211; Page 537<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Cumulative_Assessment\">Solving Quadratic Equations Cumulative Assessment &#8211; Page(538-539)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Solving_Quadratic_Equations_Maintaining_Mathematical_Proficiency\"><\/a>Solving Quadratic Equations Maintaining Mathematical Proficiency<\/h3>\n<p><strong>Factor the trinomial.<\/strong><br \/>\nQuestion 1.<br \/>\nx<sup>2<\/sup> + 10x + 25<br \/>\nAnswer:<br \/>\nx\u00b2 + 10x + 25<br \/>\na\u00b2 + 2ab + b\u00b2 = (a + b )\u00b2<br \/>\nx\u00b2 + 10x + 25 = x\u00b2 + 2 (5) (x) + 5\u00b2<br \/>\na = x and b = 5<br \/>\nx\u00b2 + 2 (5) (x) + 5\u00b2 = (x + 5)\u00b2<\/p>\n<p>Question 2.<br \/>\nx<sup>2<\/sup> &#8211; 20x + 100<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 20x + 100<br \/>\na\u00b2 &#8211; 2ab + b\u00b2 = (a &#8211; b )\u00b2<br \/>\nx\u00b2 &#8211; 20x + 100 = x\u00b2 &#8211; 2 (10) (x) + 10\u00b2<br \/>\na = x and b = 10<br \/>\nx\u00b2 &#8211; 2 (10) (x) + 10\u00b2 = (x &#8211; 10)\u00b2<\/p>\n<p>Question 3.<br \/>\nx<sup>2<\/sup> + 12x + 36<br \/>\nAnswer:<br \/>\nx\u00b2 + 12x + 36<br \/>\na\u00b2 + 2ab + b\u00b2 = (a + b )\u00b2<br \/>\nx\u00b2 + 12x + 36 = x\u00b2 + 2 (6) (x) + 6\u00b2<br \/>\na = x and b = 6<br \/>\nx\u00b2 + 2 (6) (x) + 6\u00b2 = (x + 6)\u00b2<\/p>\n<p>Question 4.<br \/>\nx<sup>2<\/sup> &#8211; 18x + 81<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 18x + 81<br \/>\na\u00b2 &#8211; 2ab + b\u00b2 = (a &#8211; b )\u00b2<br \/>\nx\u00b2 &#8211; 18x + 81 = x\u00b2 &#8211; 2 (9) (x) + 9\u00b2<br \/>\na = x and b = 9<br \/>\nx\u00b2 &#8211; 2 (9) (x) + 9\u00b2 = (x &#8211; 9)\u00b2<\/p>\n<p>Question 5.<br \/>\nx<sup>2<\/sup> + 16x + 64<br \/>\nAnswer:<br \/>\nx\u00b2 + 16x + 64<br \/>\na\u00b2 + 2ab + b\u00b2 = (a + b )\u00b2<br \/>\nSo,<br \/>\nx\u00b2 + 16x + 64 = x\u00b2 + 2 (8) (x) + 8\u00b2<br \/>\na = x and b = 8<br \/>\nx\u00b2 + 2 (8) (x) + 8\u00b2 = (x + 8)\u00b2<\/p>\n<p>Question 6.<br \/>\nx<sup>2<\/sup> &#8211; 30x + 225<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 30x + 225<br \/>\na\u00b2 &#8211; 2ab + b\u00b2 = (a &#8211; b )\u00b2<br \/>\nx\u00b2 &#8211; 30x + 225<br \/>\n= x\u00b2 &#8211; 2 (15) (x) + 15\u00b2<br \/>\na = x and b = 15<br \/>\nx\u00b2 &#8211; 2 (15) (x) + 15\u00b2 = (x &#8211; 15)\u00b2<\/p>\n<p><strong>Solve the system of linear equations by graphing.<\/strong><br \/>\nQuestion 7.<br \/>\ny = -5x + 3<br \/>\ny = 2x &#8211; 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-106567\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9.png\" alt=\"\" width=\"481\" height=\"507\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9.png 481w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-285x300.png 285w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\nFrom the graph, the intersection point of the given system of linear equations is (1, -2)<\/p>\n<p>Question 8.<br \/>\ny = \\(\\frac{3}{2}\\)x &#8211; 2<br \/>\ny = &#8211;\\(\\frac{1}{4}\\)x + 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-106570\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-1.png\" alt=\"\" width=\"486\" height=\"517\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-1.png 486w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-1-282x300.png 282w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><br \/>\nFrom the graph, the intersection point of the given system of linear equations is (4, 4)<\/p>\n<p>Question 9.<br \/>\ny = \\(\\frac{1}{2}\\)x + 4<br \/>\ny = -3x &#8211; 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-106573\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-2.png\" alt=\"\" width=\"488\" height=\"531\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-2.png 488w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-2-276x300.png 276w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><br \/>\nFrom the graph, the intersection point of the given system of linear equations is (-2, 3)<\/p>\n<p>Question 10.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nWhat value of c makes x<sup>2<\/sup> + bx + c a perfect square trinomial?<br \/>\nAnswer:<br \/>\nx\u00b2 + bx + c<br \/>\nTo make the given linear equation a perfect square trinomial,<br \/>\nThe value of c must be a square<br \/>\nFor perfect square trinomials,<br \/>\nWe compare the equation with<br \/>\na\u00b2 + 2ab + b\u00b2<br \/>\nx\u00b2 + 2 (\\(\\frac{b}{2}\\)) (x) + c<br \/>\nc = \\(\\frac{b}{2}\\)<br \/>\nThe value of c to make the given linear equation a perfect square trinomial is \\(\\frac{b}{2}\\)<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Mathematical_Practices\"><\/a>Solving Quadratic Equations Mathematical Practices<\/h3>\n<p>Mathematically proficient students monitor their work and change course as needed.<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nUse the graph in Example 1 to approximate the negative solution of the equation x<sup>2<\/sup> + x &#8211; 1 = 0 to the nearest thousandth.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-106597\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-3.png\" alt=\"\" width=\"160\" height=\"103\" \/><br \/>\nAnswer:<br \/>\nx\u00b2 + x &#8211; 1 = 0<br \/>\nWe can estimate the approximate solution of the given equation is 0.65<br \/>\nx = 0.65,<br \/>\n(0.65)\u00b2 + 0.65 &#8211; 1 = 0.0725<br \/>\nFor x = 0.64,<br \/>\nThe approximate value of the given equation is<br \/>\n(0.64)\u00b2 + 0.64 &#8211; 1 = 0.0496<br \/>\nFor x = 0.63,<br \/>\nThe approximate value of the given equation is<br \/>\n(0.63)\u00b2 + 0.63 &#8211; 1 = 0.0269<br \/>\nFor x = 0.62,<br \/>\nThe approximate value of the given equation is<br \/>\n(0.62)\u00b2 + 0.62 &#8211; 1 = 0.0044<br \/>\nFor x = 0.61,<br \/>\nThe approximate value of the given equation is<br \/>\n(0.61)\u00b2 + 0.61 &#8211; 1 = -0.0179<br \/>\nFor x = 0.60,<br \/>\nThe approximate value of the given equation is<br \/>\n(0.60)\u00b2 + 0.60 &#8211; 1 = -0.04<br \/>\nFor x = 0.59,<br \/>\nThe approximate value of the given equation is<br \/>\n(0.59)\u00b2 + 0.59 &#8211; 1 = -0.0619<br \/>\nThus the negative solution of the given equation is 0.61<\/p>\n<p>Question 2.<br \/>\nThe graph of y = x<sup>2<\/sup> + x &#8211; 3 is shown. Approximate both solutions of the equation x<sup>2<\/sup> + x &#8211; 3 = 0 to the nearest thousandth.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35269\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 1\" width=\"167\" height=\"119\" \/><br \/>\nAnswer:<br \/>\ny = x\u00b2 + x &#8211; 3<br \/>\nThe approximate positive solution of the given equation is 1.60<br \/>\nThe approximate negative solution of the given equation is 2.2<br \/>\nFor the positive solution of the given equation<br \/>\nFor x = 1.60,<br \/>\nThe approximate value of the given equation is<br \/>\n(1.60)\u00b2 + 1.60 &#8211; 3 = 1.162<br \/>\nFor x = 1.59,<br \/>\nThe approximate value of the given equation is<br \/>\n(1.59)\u00b2 + 1.59 &#8211; 3 = 1.118<br \/>\nFor x = 1.30,<br \/>\nThe approximate value of the given equation is<br \/>\n(1.30)\u00b2 + 1.30 &#8211; 3 = -0.01<br \/>\nThe positive solution of the given equation is 1.30<br \/>\nFor the negative solution of the given equation<br \/>\nFor x = 2.20,<br \/>\nThe approximate value of the given equation is<br \/>\n(2.20)\u00b2 + 2.20 &#8211; 3 = 4.040<br \/>\nFor x = 2.10,<br \/>\nThe approximate value of the given equation is<br \/>\n(2.10)\u00b2 + 2.10 &#8211; 3 = 3.510<br \/>\nFor x = 1.90,<br \/>\nThe approximate value of the given equation is<br \/>\n(1.90)\u00b2 + 1.90 &#8211; 3 = 2.510<br \/>\nFor x = 1.20,<br \/>\nThe approximate value of the given equation is<br \/>\n(1.20)\u00b2 + 1.20 &#8211; 3 = -0.360<br \/>\nThus the negative solution of the given equation is: 1.90<\/p>\n<h3><a id=\"Lesson_9.1_Properties_of_Radicals\"><\/a>Lesson 9.1 Properties of Radicals<\/h3>\n<p><strong>Essential Question<\/strong><br \/>\nHow can you multiply and divide square roots?<br \/>\nAnswer:<br \/>\nYou can multiply and divide square roots by using the &#8220;Product Rule&#8221; and &#8220;Quotient Rule&#8221;<br \/>\n\\(\\sqrt{a}\\) \u22c5 \\(\\sqrt{b}\\) = \\(\\sqrt{{a}\\cdot b}\\)<br \/>\n\\(\\frac{\\sqrt{a}}{\\sqrt{b}}\\) = \\(\\sqrt{\\frac{a}{b}}\\)<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Operations with Square Roots<br \/>\nWork with a partner. For each operation with square roots, compare the results obtained using the two indicated orders of operations. What can you conclude?<br \/>\na. Square Roots and Addition<br \/>\nIs \\(\\sqrt{36}\\) + \\(\\sqrt{64}\\) equal to \\(\\sqrt{36+64}\\)?<br \/>\nIn general, is \\(\\sqrt{a}\\) + \\(\\sqrt{b}\\) equal to \\(\\sqrt{a+b}\\)? Explain your reasoning.<br \/>\nAnswer:<br \/>\n\\(\\sqrt{36}\\) + \\(\\sqrt{64}\\) = \\(\\sqrt{36 + 64}\\)<br \/>\n\\(\\sqrt{a}\\) + \\(\\sqrt{b}\\) and \\(\\sqrt{a + b}\\)<br \/>\na = 36 and b = 64<br \/>\n\\(\\sqrt{36}\\) + \\(\\sqrt{64}\\)<br \/>\n= 6 + 8<br \/>\n= 14<br \/>\n\\(\\sqrt{36 + 64}\\)<br \/>\n= \\(\\sqrt{100}\\)<br \/>\n= 10<br \/>\n\\(\\sqrt{a}\\) + \\(\\sqrt{b}\\) \u2260 \\(\\sqrt{a + b}\\)<\/p>\n<p>b. Square Roots and Multiplications<br \/>\n\\(\\sqrt{4}\\) \u2022 \\(\\sqrt{9}\\) equal to \\(\\sqrt{{4} \\cdot 9}\\)?<br \/>\nIn general, is \\(\\sqrt{a}\\) \u2022 \\(\\sqrt{b}\\) equal to \\(\\sqrt{{a} \\cdot b}\\)? Explain your reasoning.<br \/>\nAnswer:<br \/>\n\\(\\sqrt{4}\\) \u22c5 \\(\\sqrt{9}\\)<br \/>\n\\(\\sqrt{{4}\\cdot9}\\)<br \/>\n\\(\\sqrt{a}\\) \u22c5 \\(\\sqrt{b}\\) and \\(\\sqrt{{a}\\cdot b}\\)<br \/>\na = 4 and b = 9<br \/>\n\\(\\sqrt{4}\\) \u22c5 \\(\\sqrt{9}\\)<br \/>\n= 2 \u22c5 3<br \/>\n= 6<br \/>\n\\(\\sqrt{{4}\\cdot 9}\\)<br \/>\n= \\(\\sqrt{36}\\)<br \/>\n= 6<br \/>\n\\(\\sqrt{a}\\) \u22c5 \\(\\sqrt{b}\\) = \\(\\sqrt{{a}\\cdot b}\\)<\/p>\n<p>c. Is \\(\\sqrt{64}\\) &#8211; \\(\\sqrt{36}\\) equal to \\(\\sqrt{64 &#8211; 36}\\)?<br \/>\nIn general, is \\(\\sqrt{a}\\) &#8211; \\(\\sqrt{b}\\) equal to \\(\\sqrt{a-b}\\)? Explain your reasoning.<br \/>\nAnswer:<br \/>\n\\(\\sqrt{64}\\) &#8211; \\(\\sqrt{36}\\)<br \/>\n\\(\\sqrt{64 &#8211; 36}\\)<br \/>\n\\(\\sqrt{a}\\) &#8211; \\(\\sqrt{b}\\) and \\(\\sqrt{a &#8211; b}\\)<br \/>\na = 64 and b = 36<br \/>\n\\(\\sqrt{64}\\) &#8211; \\(\\sqrt{36}\\)<br \/>\n= 8 &#8211; 6<br \/>\n= 2<br \/>\n\\(\\sqrt{64 &#8211; 36}\\)<br \/>\n= \\(\\sqrt{28}\\)<br \/>\n= 5.291<br \/>\n\\(\\sqrt{a}\\) &#8211; \\(\\sqrt{b}\\) \u2260 \\(\\sqrt{a &#8211; b}\\)<\/p>\n<p>d. Square Roots and Division<br \/>\nIs \\(\\frac{\\sqrt{100}}{\\sqrt{4}}\\) equal to \\(\\sqrt{\\frac{100}{4}}\\)?<br \/>\nIn general, is \\(\\frac{\\sqrt{a}}{\\sqrt{b}}\\) equal to \\(\\sqrt{\\frac{a}{b}}\\)? Explain your reasoning.<br \/>\nAnswer:<br \/>\n\\(\\frac{\\sqrt{100}}{\\sqrt{4}}\\)<br \/>\n\\(\\sqrt{\\frac{100}{4}}\\)<br \/>\n\\(\\frac{\\sqrt{a}}{\\sqrt{b}}\\)\u00a0 and \\(\\sqrt{\\frac{a}{b}}\\)<br \/>\na = 100 and b = 4<br \/>\n\\(\\frac{\\sqrt{100}}{\\sqrt{4}}\\)<br \/>\n= \\(\\frac{10}{2}\\)<br \/>\n= 5<br \/>\n\\(\\sqrt{\\frac{100}{4}}\\)<br \/>\n= \\(\\sqrt{25}\\)<br \/>\n= 5<br \/>\n\\(\\frac{\\sqrt{a}}{\\sqrt{b}}\\) = \\(\\sqrt{\\frac{a}{b}}\\)<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Writing Counterexamples<br \/>\nWork with a partner. A counterexample is an example that proves that a general statement is not true. For each general statement in Exploration 1 that is not true, write a counterexample different from the example given.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35270\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 1\" width=\"228\" height=\"131\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you multiply and divide square roots?<br \/>\nAnswer:<br \/>\nYou can multiply and divide square roots by using the &#8220;Product Rule&#8221; and &#8220;Quotient Rule&#8221;<br \/>\n\\(\\sqrt{a}\\) \u22c5 \\(\\sqrt{b}\\) = \\(\\sqrt{{a}\\cdot b}\\)<br \/>\n\\(\\frac{\\sqrt{a}}{\\sqrt{b}}\\) = \\(\\sqrt{\\frac{a}{b}}\\)<\/p>\n<p>Question 4.<br \/>\nGive an example of multiplying square roots and an example of dividing square roots that are different from the examples in Exploration 1.<br \/>\nAnswer:<br \/>\nWe use the &#8220;Product Rule&#8221; for the multiplication of square roots<br \/>\n\\(\\sqrt{a}\\) \u22c5 \\(\\sqrt{b}\\) = \\(\\sqrt{{a}\\cdot b}\\)<br \/>\nThe values of a and b are:<br \/>\na = 144 and b = 36<br \/>\n\\(\\sqrt{144}\\) \u22c5 \\(\\sqrt{36}\\)<br \/>\n= 12 \u22c5 6<br \/>\n= 72<br \/>\n\\(\\sqrt{{144}\\cdot 36}\\)<br \/>\n= \\(\\sqrt{5,184}\\)<br \/>\n= 72<br \/>\nThe quotient rule is:<br \/>\n\\(\\frac{\\sqrt{a}}{\\sqrt{b}}\\) = \\(\\sqrt{\\frac{a}{b}}\\)<br \/>\na = 144 and b = 36<br \/>\n\\(\\frac{\\sqrt{144}}{\\sqrt{36}}\\)<br \/>\n= \\(\\frac{12}{6}\\)<br \/>\n= 2<br \/>\n\\(\\sqrt{\\frac{144}{36}}\\)<br \/>\n= \\(\\sqrt{\\frac{12}{3}}\\)<br \/>\n= \\(\\sqrt{4}\\)<br \/>\n= 2<\/p>\n<p>Question 5.<br \/>\nWrite an algebraic rule for each operation.<br \/>\na. the product of square roots<br \/>\nb. the quotient of square roots<br \/>\nAnswer:<br \/>\nThe algebraic rule for the product of square roots<br \/>\n\\(\\sqrt{a}\\) \u22c5 \\(\\sqrt{b}\\) = \\(\\sqrt{{a}\\cdot b}\\)<br \/>\nThe algebraic rule for the division of square roots is<br \/>\n\\(\\frac{\\sqrt{a}}{\\sqrt{b}}\\) = \\(\\sqrt{\\frac{a}{b}}\\)<\/p>\n<h3>9.1 Exercise<\/h3>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\sqrt{24}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{24}\\)<br \/>\n\\(\\sqrt{{a}\\cdot b}\\) = \\(\\sqrt{a}\\) \u22c5 \\(\\sqrt{b}\\)<br \/>\n\\(\\sqrt{24}\\)<br \/>\n= \\(\\sqrt{{4}\\cdot 6}\\)<br \/>\n= \\(\\sqrt{4}\\) \u22c5 \\(\\sqrt{6}\\)<br \/>\n= 2 \\(\\sqrt{6}\\)<br \/>\n\\(\\sqrt{24}\\) = 2 \\(\\sqrt{6}\\)<\/p>\n<p>Question 2.<br \/>\n&#8211;\\(\\sqrt{80}\\)<br \/>\nAnswer:<br \/>\n&#8211;\\(\\sqrt{80}\\)<br \/>\n\\(\\sqrt{{a}\\cdot b}\\) = \\(\\sqrt{a}\\) \u22c5 \\(\\sqrt{b}\\)<br \/>\n&#8211;\\(\\sqrt{80}\\)<br \/>\n= &#8211;\\(\\sqrt{{16}\\cdot 5}\\)<br \/>\n= &#8211;\\(\\sqrt{16}\\) \u22c5 \\(\\sqrt{5}\\)<br \/>\n= -4 \\(\\sqrt{5}\\)<br \/>\n&#8211;\\(\\sqrt{80}\\) = -4 \\(\\sqrt{5}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt{49 x^{3}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{49 x^{3}}\\)<br \/>\n\\(\\sqrt{{a}\\cdot b}\\) = \\(\\sqrt{a}\\) \u22c5 \\(\\sqrt{b}\\)<br \/>\n\\(\\sqrt{49 x^{3}}\\)<br \/>\n= \\(\\sqrt{{49 x^{2}}\\cdot x}\\)<br \/>\n= \\(\\sqrt{49 x^{2}}\\) \u22c5 \\(\\sqrt{x}\\)<br \/>\n= 7x \\(\\sqrt{x}\\)<\/p>\n<p>Question 4.<br \/>\n\\(\\sqrt{49 n^{5}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{49 n^{5}}\\)<br \/>\n\\(\\sqrt{{a}\\cdot b}\\) = \\(\\sqrt{a}\\) \u22c5 \\(\\sqrt{b}\\)<br \/>\n\\(\\sqrt{49 n^{5}}\\)<br \/>\n= \\(\\sqrt{{49 n^{4}}\\cdot n}\\)<br \/>\n= \\(\\sqrt{49 n^{4}}\\) \u22c5 \\(\\sqrt{n}\\)<br \/>\n= 7n\u00b2 \\(\\sqrt{n}\\)<\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 5.<br \/>\n\\(\\sqrt{\\frac{23}{9}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{\\frac{23}{9}}\\)<br \/>\n\\(\\frac{\\sqrt{a}}{\\sqrt{b}}\\) = \\(\\sqrt{\\frac{a}{b}}\\)<br \/>\n\\(\\sqrt{\\frac{23}{9}}\\)<br \/>\n= \\(\\sqrt{\\frac{23}{9}}\\)<br \/>\n= \\(\\frac{\\sqrt{23}}{\\sqrt{9}}\\)<br \/>\n= \\(\\frac{\\sqrt{23}}{3}\\)<\/p>\n<p>Question 6.<br \/>\n&#8211;\\(\\sqrt{\\frac{17}{100}}\\)<br \/>\nAnswer:<br \/>\n&#8211;\\(\\sqrt{\\frac{17}{100}}\\)<br \/>\n\\(\\frac{\\sqrt{a}}{\\sqrt{b}}\\) = \\(\\sqrt{\\frac{a}{b}}\\)<br \/>\n&#8211;\\(\\sqrt{\\frac{17}{100}}\\)<br \/>\n= &#8211;\\(\\sqrt{\\frac{17}{100}}\\)<br \/>\n= &#8211;\\(\\frac{\\sqrt{17}}{\\sqrt{100}}\\)<br \/>\n= &#8211;\\(\\frac{\\sqrt{17}}{10}\\)<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt{\\frac{36}{z^{2}}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{\\frac{36}{z^{2}}}\\)<br \/>\n\\(\\frac{\\sqrt{a}}{\\sqrt{b}}\\) = \\(\\sqrt{\\frac{a}{b}}\\)<br \/>\n\\(\\sqrt{\\frac{36}{z^{2}}}\\)<br \/>\n= \\(\\sqrt{\\frac{36}{z^{2}}}\\)<br \/>\n= \\(\\frac{\\sqrt{36}}{\\sqrt{z^{2}}}\\)<br \/>\n= \\(\\frac{6}{z}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt{\\frac{4 x^{2}}{64}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{\\frac{4 x^{2}}{64}}\\)<br \/>\n\\(\\frac{\\sqrt{a}}{\\sqrt{b}}\\) = \\(\\sqrt{\\frac{a}{b}}\\)<br \/>\n\\(\\sqrt{\\frac{4 x^{2}}{64}}\\)<br \/>\n= \\(\\sqrt{\\frac{4 x^{2}}{64}}\\)<br \/>\n= \\(\\frac{\\sqrt{4 x^{2}}}{\\sqrt{64}}\\)<br \/>\n= \\(\\frac{2x}{8}\\)<br \/>\n= \\(\\frac{x}{4}\\)<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt[3]{54}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt[3]{54}\\)<br \/>\n\\(\\sqrt[3]{a}{b}\\) = \\(\\sqrt[3]{a}\\) \u22c5 \\(\\sqrt[3]{b}\\)<br \/>\n\\(\\sqrt[3]{54}\\)<br \/>\n= \\(\\sqrt[3]{54}{1}\\)<br \/>\n= \\(\\sqrt[3]{54}\\) \u22c5 \\(\\sqrt[3]{1}\\)<br \/>\n= \\(\\sqrt[3]{27 \u00d7 2}\\)<br \/>\n= \\(\\sqrt[3]{27}\\) \u22c5 \\(\\sqrt[3]{2}\\)<br \/>\n= 3\\(\\sqrt[3]{2}\\)<\/p>\n<p>Question 10.<br \/>\n\\(\\sqrt[3]{16 x^{4}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt[3]{16 x^{4}}\\)<br \/>\n\\(\\sqrt[3]{a}{b}\\) = \\(\\sqrt[3]{a}\\) \u22c5 \\(\\sqrt[3]{b}\\)<br \/>\n\\(\\sqrt[3]{16 x^{4}}\\)<br \/>\n= \\(\\sqrt[3]{x^{3}}{16x}\\)<br \/>\n= \\(\\sqrt[3]{x^{3}}\\) \u22c5 \\(\\sqrt[3]{16x}\\)<br \/>\n= x\\(\\sqrt[3]{16x}\\)<\/p>\n<p>Question 11.<br \/>\n\\(\\sqrt[3]{\\frac{a}{-27}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt[3]{\\frac{a}{-27}}\\)<br \/>\n\\(\\sqrt[3]{\\frac{a}{b}}\\) = \\(\\sqrt[3]{a}\\) \/ \\(\\sqrt[3]{b}\\)<br \/>\n\\(\\sqrt[3]{\\frac{a}{-27}}\\)<br \/>\n= \\(\\sqrt[3]{a}\\) \/ \\(\\sqrt[3]{-27}\\)<br \/>\n=\\(\\sqrt[3]{a}\\) \/ \\(\\sqrt[3]{-3^{3}}\\)<br \/>\n= &#8211;\\(\\sqrt[3]{a}\\) \/ 3<\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt[3]{\\frac{25 c^{7} d^{3}}{64}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt[3]{\\frac{25 c^{7} d^{3}}{64}}\\)<br \/>\n\\(\\sqrt[3]{\\frac{a}{b}}\\) = \\(\\sqrt[3]{a}\\) \/ \\(\\sqrt[3]{b}\\)<br \/>\n\\(\\sqrt[3]{\\frac{25 c^{7} d^{3}}{64}}\\)<br \/>\n= \\(\\sqrt[3]{25 c^{7} d^{3}}\\) \/ \\(\\sqrt[3]{64}\\)<br \/>\n=\\(\\sqrt[3]{25 c^{3} c^{4} d^{3}}\\) \/ \\(\\sqrt[3]{4^{3}}\\)<br \/>\n= c\u00b2d\\(\\sqrt[3]{25c}\\) \/ 4<\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 13.<br \/>\n\\(\\frac{1}{\\sqrt{5}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{\\sqrt{5}}\\)<br \/>\n= \\(\\frac{1}{\\sqrt{5}}\\) \u00d7 (\\(\\sqrt{5}\\) \/ \\(\\sqrt{5}\\))<br \/>\n= \\(\\sqrt{5}\\) \/ (\\(\\sqrt{5}\\) \u00d7 \\(\\sqrt{5}\\))<br \/>\n= \\(\\sqrt{5}\\) \/ 5<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{\\sqrt{10}}{\\sqrt{3}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{\\sqrt{10}}{\\sqrt{3}}\\)<br \/>\n\\(\\frac{\\sqrt{10}}{\\sqrt{3}}\\)<br \/>\n= \\(\\frac{\\sqrt{10}}{\\sqrt{3}}\\) \u00d7 (\\(\\sqrt{3}\\) \/ \\(\\sqrt{3}\\))<br \/>\n= \\(\\sqrt{10 \u00d7 3}\\) \/ (\\(\\sqrt{3}\\) \u00d7 \\(\\sqrt{3}\\))<br \/>\n= \\(\\sqrt{30}\\) \/ 3<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{7}{\\sqrt{2 x}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{7}{\\sqrt{2 x}}\\)<br \/>\n\\(\\frac{7}{\\sqrt{2 x}}\\)<br \/>\n= \\(\\frac{7}{\\sqrt{2 x}}\\) \u00d7 (\\(\\sqrt{2 x}\\) \/ \\(\\sqrt{2 x}\\))<br \/>\n= 7\\(\\sqrt{2 x}\\) \/ (\\(\\sqrt{2 x}\\) \u00d7 \\(\\sqrt{2 x}\\))<br \/>\n= 7\\(\\sqrt{2 x}\\) \/ 2x<\/p>\n<p>Question 16.<br \/>\n\\(\\sqrt{\\frac{2 y^{2}}{3}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{\\frac{2 y^{2}}{3}}\\)<br \/>\n\\(\\sqrt{\\frac{2 y^{2}}{3}}\\)<br \/>\n= \\(\\frac{\\sqrt{2 y^{2}}}{\\sqrt{3}}\\)<br \/>\n\\(\\frac{\\sqrt{2 y^{2}}}{\\sqrt{3}}\\)<br \/>\n= \\(\\frac{\\sqrt{2 y^{2}}}{\\sqrt{3}}\\) \u00d7 (\\(\\sqrt{3}\\) \/ \\(\\sqrt{3}\\))<br \/>\n= \\(\\sqrt{2 y^{2} \u00d7 3}\\) \/ (\\(\\sqrt{3}\\) \u00d7 \\(\\sqrt{3}\\))<br \/>\n= y\\(\\sqrt{6}\\) \/ 3<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{5}{\\sqrt[3]{32}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{5}{\\sqrt[3]{32}}\\)<br \/>\n= \\(\\frac{5}{\\sqrt[3]{32}}\\) \u00d7 (\\(\\sqrt[3]{2}\\) \/ \\(\\sqrt[3]{2}\\))<br \/>\n= 5\\(\\sqrt[3]{2}\\) \/ (\\(\\sqrt[3]{32}\\) \u00d7 \\(\\sqrt[3]{2}\\))<br \/>\n= 5\\(\\sqrt[3]{2}\\) \/ 4<\/p>\n<p>Question 18.<br \/>\n\\(\\frac{8}{1+\\sqrt{3}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{8}{1 + \\sqrt{3}}\\)<br \/>\n\\(\\frac{8}{1 + \\sqrt{3}}\\)<br \/>\n= \\(\\frac{8}{1 + \\sqrt{3}}\\) \u00d7 (\\(1 &#8211; \\sqrt{3}\\) \/ \\(1 &#8211; \\sqrt{3}\\))<br \/>\n= 8\\((1 &#8211; \\sqrt{3})\\) \/ (\\(1 + \\sqrt{3}\\) \u00d7 \\(1 &#8211; \\sqrt{3}\\))<br \/>\n= 8\\((1 &#8211; \\sqrt{3})\\) \/ -2<br \/>\n= &#8211; 8\\((1 &#8211; \\sqrt{3})\\) \/ 2<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{\\sqrt{13}}{\\sqrt{5}-2}\\)<br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n\\(\\frac{\\sqrt{13}}{\\sqrt{5}-2}\\)<br \/>\nTo rationalize the denominator, multiply and divide the given fraction with \\(\\sqrt{5} + 2\\)<br \/>\n\\(\\frac{\\sqrt{13}}{\\sqrt{5}-2}\\)<br \/>\n= \\(\\frac{\\sqrt{13}}{\\sqrt{5}-2}\\) \u00d7 (\\( \\sqrt{5} &#8211; 2\\) \/ \\( \\sqrt{5} &#8211; 2\\))<br \/>\n= 13(\\(\\sqrt{{5}} &#8211; 2\\)) \/ (\\( \\sqrt{5} &#8211; 2\\) \u00d7 \\( \\sqrt{5} + 2\\))<br \/>\n= 13(\\(\\sqrt{{5}} &#8211; 2\\)) \/ -1<br \/>\n= &#8211; 13(\\(\\sqrt{{5}} &#8211; 2\\))<\/p>\n<p>Question 20.<br \/>\n\\(\\frac{12}{\\sqrt{2}+\\sqrt{7}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{12}{\\sqrt{2}+\\sqrt{7}}\\)<br \/>\nTo rationalize the denominator, multiply and divide the given fraction with \\(\\sqrt{2} -\\sqrt{7} \\)<br \/>\n\\(\\frac{12}{\\sqrt{2}+\\sqrt{7}}\\)<br \/>\n= \\(\\frac{12}{\\sqrt{2}+\\sqrt{7}}\\) \u00d7 (\\(\\sqrt{2} -\\sqrt{7} \\) \/ \\(\\sqrt{2} -\\sqrt{7} \\))<br \/>\n= 12(\\(\\sqrt{2} -\\sqrt{7} \\)) \/ (\\(\\sqrt{2} +\\sqrt{7} \\) \u00d7 \\(\\sqrt{2} -\\sqrt{7} \\))<br \/>\n= 12(\\(\\sqrt{2} -\\sqrt{7}\\)) \/ -5<br \/>\n= &#8211; 12(\\(\\sqrt{2} -\\sqrt{7} \\))\/ 5<\/p>\n<p>Question 21.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 6, how far can you see when your eye level is 35 feet above the water?<br \/>\nAnswer:<br \/>\nIn Example 6,<br \/>\nIt is given that<br \/>\nd = \\(\\sqrt{\\frac{3h}{2}}\\)<br \/>\nWhere,<br \/>\n&#8216;h&#8217; is the height that your eye can see above the water<br \/>\n&#8216;d&#8217; is the distance your eye can see<br \/>\nh = 35 feet<br \/>\nd = \\(\\sqrt{\\frac{3 \u00d7105}{2}}\\)<br \/>\nd = \\(\\sqrt{\\frac{315}{2}}\\)<br \/>\n\\(\\sqrt{\\frac{a}{b}}\\) = \\(\\frac{\\sqrt{a}}{\\sqrt{b}}\\)<br \/>\n\\(\\sqrt{\\frac{315}{2}}\\)<br \/>\n= \\(\\frac{\\sqrt{315}}{\\sqrt{2}}\\)<br \/>\nTo rationalize the denominator, multiply and divide the given fraction with \\(\\sqrt{2}\\)<br \/>\n\\(\\sqrt{\\frac{315}{2}}\\)<br \/>\n= \\(\\frac{\\sqrt{315}}{\\sqrt{2}}\\) \u00d7 (\\(\\sqrt{2}\\) \/ \\(\\sqrt{2}\\))<br \/>\n= \\(\\sqrt{315 \u00d7 2}\\) \/ (\\(\\sqrt{2}\\) \u00d7 \\(\\sqrt{2}\\))<br \/>\n= \\(\\sqrt{630}\\) \/ 2<br \/>\n= 12.54 feet<\/p>\n<p>Question 22.<br \/>\nThe dimensions of a dance floor form a golden rectangle. The ratio of the length to the width of the golden rectangle is \\(1 + \\sqrt{5}\\) : 2. The longer side of the dance floor is 50 feet. What is the length of the shorter side of the dance floor?<br \/>\nAnswer:<br \/>\nThe dimensions of a dance floor form a golden rectangle.<br \/>\nThe ratio of the length to the width of the golden rectangle is \\(1 + \\sqrt{5}\\) : 2.<br \/>\nThe longer side of the dance floor is 50 feet.<br \/>\n\\(\\frac{1+\\sqrt{5}}{2}\\) = \\(\\frac{50}{h}\\)<br \/>\nh (\\(1 + \\sqrt{5}\\)) = 50 \u00d7 2<br \/>\nh (\\(1 + \\sqrt{5}\\)) = 100<br \/>\nh = \\(\\frac{100}{1 + \\sqrt{5}}\\)<br \/>\nTo rationalize the denominator, multiply and divide the given fraction with \\(1 &#8211; \\sqrt{5}\\)<br \/>\n\\(\\frac{100}{1 + \\sqrt{5}}\\)<br \/>\n= \\(\\frac{100}{1 + \\sqrt{5}}\\) \u00d7 (\\(1 &#8211; \\sqrt{5}\\) \/ \\(1 &#8211; \\sqrt{5}\\))<br \/>\n= 100\\((1 &#8211; \\sqrt{5})\\) \/ (\\(1 + \\sqrt{5}\\) \u00d7 \\(1 &#8211; \\sqrt{5}\\))<br \/>\n= 100\\((1 &#8211; \\sqrt{5})\\) \/ -4<br \/>\n= &#8211; 100\\((1 &#8211; \\sqrt{5})\\) \/ 4<br \/>\n= 30.90 feet<\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 23.<br \/>\n3\\(\\sqrt{2}\\) &#8211; \\(\\sqrt{6}\\) + 10\\(\\sqrt{2}\\)<br \/>\nAnswer:<br \/>\n3\\(\\sqrt{2}\\) &#8211; \\(\\sqrt{6}\\) + 10\\(\\sqrt{2}\\)<br \/>\n= \\(\\sqrt{2}\\) (3 + 10) &#8211; \\(\\sqrt{6}\\)<br \/>\n= \\(\\sqrt{2}\\) (13) &#8211; \\(\\sqrt{6}\\)<br \/>\n= 13\\(\\sqrt{2}\\) &#8211; \\(\\sqrt{6}\\)<\/p>\n<p>Question 24.<br \/>\n4\\(\\sqrt{7}\\) &#8211; 6\\(\\sqrt{63}\\)<br \/>\nAnswer:<br \/>\n4\\(\\sqrt{7}\\) &#8211; 6\\(\\sqrt{63}\\)<br \/>\n= 4\\(\\sqrt{7}\\) &#8211; 6\\(\\sqrt{7 \u00d7 9}\\)<br \/>\n= 4\\(\\sqrt{7}\\) &#8211; 6 (3)\\(\\sqrt{7}\\)<br \/>\n= 4\\(\\sqrt{7}\\) &#8211; 18\\(\\sqrt{7}\\)<br \/>\n= \\(\\sqrt{7}\\) ( 4 &#8211; 18)<br \/>\n= \\(\\sqrt{7}\\) (-14)<br \/>\n= -14\\(\\sqrt{7}\\)<\/p>\n<p>Question 25.<br \/>\n4\\(\\sqrt [3]{ 5x }\\) &#8211; 11\\(\\sqrt [3]{ 5x }\\)<br \/>\nAnswer:<br \/>\n4\\(\\sqrt [3]{ 5x }\\) &#8211; 11\\(\\sqrt [3]{ 5x }\\)<br \/>\n= \\(\\sqrt [3]{ 5x }\\) (4 &#8211; 11)<br \/>\n= \\(\\sqrt [3]{ 5x }\\) (-7)<br \/>\n= -7\\(\\sqrt [3]{ 5x }\\)<\/p>\n<p>Question 26.<br \/>\n\\(\\sqrt{3}\\)(8\\(\\sqrt{2}\\) + 7\\(\\sqrt{32}\\))<br \/>\nAnswer:<br \/>\n\\(\\sqrt{3}\\)(8\\(\\sqrt{2}\\) + 7\\(\\sqrt{32}\\))<br \/>\n= \\(\\sqrt{3}\\)(8\\(\\sqrt{2}\\) + 7\\(\\sqrt{16 \u00d7 2}\\))<br \/>\n= \\(\\sqrt{3}\\)(8\\(\\sqrt{2}\\) + 7 (4)\\(\\sqrt{2}\\))<br \/>\n= \\(\\sqrt{3}\\)(8\\(\\sqrt{2}\\) + 28\\(\\sqrt{2}\\))<br \/>\n= \\(\\sqrt{3}\\)(\\(\\sqrt{2}\\) (8 + 28))<br \/>\n= \\(\\sqrt{3}\\)(\\(\\sqrt{2}\\) (36))<br \/>\n= 36(\\(\\sqrt{3}\\))(\\(\\sqrt{2}\\) )<br \/>\n= 36\\(\\sqrt{6}\\)<\/p>\n<p>Question 27.<br \/>\n(2\\(\\sqrt{5}\\) &#8211; 4)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n(2\\(\\sqrt{5}\\) &#8211; 4)\u00b2<br \/>\n(a &#8211; b)\u00b2 = a\u00b2 &#8211; 2ab + b\u00b2<br \/>\na = 2\\(\\sqrt{5}\\) and b = 4<br \/>\n(2\\(\\sqrt{5}\\) &#8211; 4)\u00b2<br \/>\n= (2\\(\\sqrt{5}\\))\u00b2 &#8211; 2 (2\\(\\sqrt{5}\\)) (4) + 4\u00b2<br \/>\n= 2\u00b2 (\\(\\sqrt{5}\\))\u00b2 &#8211; 16\\(\\sqrt{5}\\) + 16<br \/>\n= 4 (5) &#8211; 16\\(\\sqrt{5}\\) + 16<br \/>\n= 20 &#8211; 16\\(\\sqrt{5}\\) + 16<br \/>\n= 20 &#8211; 16 (1 &#8211; \\(\\sqrt{5}\\))<\/p>\n<p>Question 28.<br \/>\n\\(\\sqrt [3]{ -4 }\\)(\\(\\sqrt [3]{ 2 }\\) &#8211; \\(\\sqrt [3]{ 16 }\\))<br \/>\nAnswer:<br \/>\n\\(\\sqrt [3]{ -4 }\\)(\\(\\sqrt [3]{ 2 }\\) &#8211; \\(\\sqrt [3]{ 16 }\\))<br \/>\n= \\(\\sqrt [3]{-4 \u00d7 2}\\) &#8211; \\(\\sqrt [3]{-4 \u00d7 16}\\)<br \/>\n= \\(\\sqrt [3]{-8}\\) &#8211; \\(\\sqrt [3]{-64}\\)<br \/>\n= -2 &#8211; (-4)<br \/>\n= -2 + 4<br \/>\n= 2<\/p>\n<h3><a id=\"Properties_of_Radicals_9.1_Exercises\"><\/a>Properties of Radicals<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe process of eliminating a radical from the denominator of a radical expression is called _______________.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41937\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 1\" width=\"598\" height=\"60\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-1.png 598w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-1-300x30.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat is the conjugate of the binomial \\(\\sqrt{6}\\) + 4?<br \/>\nAnswer:<br \/>\n\\(\\sqrt{6}\\) + 4<br \/>\nThe binomial conjugate of \\(\\sqrt{6}\\) + 4 is \\(\\sqrt{6}\\) &#8211; 4<\/p>\n<p>Question 3.<br \/>\n<strong>WRITING<\/strong><br \/>\nAre the expressions \\(\\frac{1}{3} \\sqrt{2 x}\\) and \\(\\sqrt{\\frac{2 x}{9}}\\) equivalent? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41938\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 3\" width=\"518\" height=\"176\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-3.png 518w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-3-300x102.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich expression does not belong with the other three? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35271\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 2\" width=\"478\" height=\"61\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-2.png 478w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-2-300x38.png 300w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-194284 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-2.png\" alt=\"Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-2\" width=\"478\" height=\"61\" \/><\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u201312, determine whether the expression is in simplest form. If the expression is not in simplest form,<\/strong> <strong>explain why.<\/strong><br \/>\nQuestion 5.<br \/>\n\\(\\sqrt{19}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41939\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 5\" width=\"371\" height=\"39\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-5.png 371w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-5-300x32.png 300w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt{\\frac{1}{7}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{\\frac{1}{7}}\\) is not in its simplest form<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt{48}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41940\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 7\" width=\"510\" height=\"62\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-7.png 510w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-7-300x36.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt{34}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{34}\\) is in its simplest form because the radicand has not any perfect square number<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{5}{\\sqrt{2}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41941\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 9\" width=\"548\" height=\"83\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-9.png 548w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-9-300x45.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 10.<br \/>\n\\(\\frac{3 \\sqrt{10}}{4}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{3 \\sqrt{10}}{4}\\) is in its simplest form<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{1}{2+\\sqrt[3]{2}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41942\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 11\" width=\"531\" height=\"97\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-11.png 531w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-11-300x55.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 12.<br \/>\n\\(6-\\sqrt[3]{54}\\)<br \/>\nAnswer:<br \/>\n\\(6-\\sqrt[3]{54}\\) is not in its simplest form because the radicand contains the perfect cube root<\/p>\n<p><strong>In Exercises 13\u201320, simplify the expression.<\/strong><br \/>\nQuestion 13.<br \/>\n\\(\\sqrt{20}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41943\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 13\" width=\"173\" height=\"107\" \/><\/p>\n<p>Question 14.<br \/>\n\\(\\sqrt{32}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{32}\\)<br \/>\n= \\(\\sqrt{2 \u00d7 16}\\)<br \/>\n= \\(\\sqrt{2}\\) \u00d7 \\(\\sqrt{16}\\)<br \/>\n= \\(\\sqrt{2}\\) \u00d7 4<br \/>\n= 4\\(\\sqrt{2}\\)<\/p>\n<p>Question 15.<br \/>\n\\(\\sqrt{128}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41944\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 15\" width=\"196\" height=\"101\" \/><\/p>\n<p>Question 16.<br \/>\n&#8211;\\(\\sqrt{72}\\)<br \/>\nAnswer:<br \/>\n&#8211;\\(\\sqrt{72}\\)<br \/>\n= &#8211;\\(\\sqrt{36 \u00d7 2}\\)<br \/>\n= &#8211;\\(\\sqrt{36}\\) \u00d7 \\(\\sqrt{2}\\)<br \/>\n= -6 \u00d7 \\(\\sqrt{2}\\)<br \/>\n= -6\\(\\sqrt{2}\\)<\/p>\n<p>Question 17.<br \/>\n\\(\\sqrt{125b}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41945\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-17.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 17\" width=\"209\" height=\"108\" \/><\/p>\n<p>Question 18.<br \/>\n\\(\\sqrt{4 x^{2}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{4 x^{2}}\\)<br \/>\n= \\(\\sqrt{(2 x)^{2}}\\)<br \/>\n= 2x<\/p>\n<p>Question 19.<br \/>\n\\(-\\sqrt{81 m^{3}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41946\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-19.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 19\" width=\"290\" height=\"104\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\sqrt{48 n^{5}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{48 n^{5}}\\)<br \/>\n= \\(\\sqrt{16 n^{4} \u00d7 3 n}\\)<br \/>\n= \\(\\sqrt{16 n^{4}}\\) \u00d7 \\(\\sqrt{3 n}\\)<br \/>\n= 4 n\u00b2 \u00d7 \\(\\sqrt{3 n}\\)<br \/>\n= 4n\u00b2\\(\\sqrt{3 n}\\)<\/p>\n<p><strong>In Exercises 21\u201328, simplify the expression.<\/strong><br \/>\nQuestion 21.<br \/>\n\\(\\sqrt{\\frac{4}{49}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41947\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-21.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 21\" width=\"161\" height=\"132\" \/><\/p>\n<p>Question 22.<br \/>\n\\(-\\sqrt{\\frac{7}{81}}\\)<br \/>\nAnswer:<br \/>\n\\(-\\sqrt{\\frac{7}{81}}\\)<br \/>\n= &#8211;\\(\\frac{\\sqrt{7}}{\\sqrt{81}}\\)<br \/>\n= &#8211;\\(\\frac{\\sqrt{7}}{9}\\)<\/p>\n<p>Question 23.<br \/>\n\\(-\\sqrt{\\frac{23}{64}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41948\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-23.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 23\" width=\"175\" height=\"133\" \/><\/p>\n<p>Question 24.<br \/>\n\\(\\sqrt{\\frac{65}{121}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{\\frac{65}{121}}\\)<br \/>\n= \\(\\frac{\\sqrt{65}}{\\sqrt{121}}\\)<br \/>\n= \\(\\frac{\\sqrt{65}}{11}\\)<\/p>\n<p>Question 25.<br \/>\n\\(\\sqrt{\\frac{a^{3}}{49}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41949\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-25.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 25\" width=\"167\" height=\"249\" \/><\/p>\n<p>Question 26.<br \/>\n\\(\\sqrt{\\frac{144}{k^{2}}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{\\frac{144}{k^{2}}}\\)<br \/>\n= \\(\\frac{\\sqrt{144}}{\\sqrt{k^{2}}}\\)<br \/>\n= \\(\\frac{12}{k}\\)<\/p>\n<p>Question 27.<br \/>\n\\(\\sqrt{\\frac{100}{4x^{2}}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41950\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-27.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 27\" width=\"174\" height=\"248\" \/><\/p>\n<p>Question 28.<br \/>\n\\(\\sqrt{\\frac{25 v^{2}}{36}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{\\frac{25v^{2}}{36}}\\)<br \/>\n= \\(\\frac{\\sqrt{25v^{2}}}{\\sqrt{36}}\\)<br \/>\n= \\(\\frac{5v}{6}\\)<\/p>\n<p><strong>In Exercises 29\u201336, simplify the expression.<\/strong><br \/>\nQuestion 29.<br \/>\n\\(\\sqrt [3]{ 16 }\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41951\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-29.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 29\" width=\"171\" height=\"108\" \/><\/p>\n<p>Question 30.<br \/>\n\\(\\sqrt [3]{ -108 }\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt [3]{ -108 }\\)<br \/>\n= \\(\\sqrt [3]{ -27 \u00d7 4 }\\)<br \/>\n= \\(\\sqrt [3]{ -27 }\\) \u00d7 \\(\\sqrt [3]{ 4 }\\)<br \/>\n= -3 \u00d7 \\(\\sqrt [3]{ 4 }\\)<br \/>\n= -3\\(\\sqrt [3]{ 4 }\\)<\/p>\n<p>Question 31.<br \/>\n\\(\\sqrt[3]{-64 x^{5}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41952\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-31.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 31\" width=\"310\" height=\"106\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-31.png 310w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-31-300x103.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/p>\n<p>Question 32.<br \/>\n&#8211;\\(\\sqrt[3]{343 n^{2}}\\)<br \/>\nAnswer:<br \/>\n&#8211;\\(\\sqrt[3]{343 n^{2}}\\)<br \/>\n= &#8211;\\(\\sqrt[3]{343 }\\) \u00d7 \\(\\sqrt[3]{ n^{2}}\\)<br \/>\n= -7 \u00d7 \\(\\sqrt[3]{ n^{2}}\\)<br \/>\n= -7\\(\\sqrt[3]{ n^{2}}\\)<\/p>\n<p>Question 33.<br \/>\n\\(\\sqrt[3]{\\frac{6 c}{-125}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41953\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-33.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 33\" width=\"199\" height=\"197\" \/><\/p>\n<p>Question 34.<br \/>\n\\(\\sqrt[3]{\\frac{8 h^{4}}{27}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt[3]{\\frac{8 h^{4}}{27}}\\)<br \/>\n= \\(\\frac{\\sqrt[3]{8 h^{4}}}{\\sqrt[3]{27}}\\)<br \/>\n= \\(\\frac{\\sqrt[3]{8 h^{3} \u00d7 h}}{\\sqrt[3]{27}}\\)<br \/>\n= \\(\\frac{2\\sqrt[3]{ h}}{3}\\)<\/p>\n<p>Question 35.<br \/>\n\\(-\\sqrt[3]{\\frac{81 y^{2}}{1000 x^{3}}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41954\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-35.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 35\" width=\"294\" height=\"309\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-35.png 294w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-35-285x300.png 285w\" sizes=\"(max-width: 294px) 100vw, 294px\" \/><\/p>\n<p>Question 36.<br \/>\n\\(\\sqrt[3]{\\frac{21}{-64 a^{3} b^{6}}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt[3]{\\frac{21}{-64 a^{3} b^{6}}}\\)<br \/>\n= \\(\\frac{\\sqrt[3]{21}}{\\sqrt[3]{-64 a^{3} b^{6}}}\\)<br \/>\n= \\(\\frac{\\sqrt[3]{21}}{\\sqrt[3]{-64 a^{3} b^{3} b^{3}}}\\)<br \/>\n= \\(\\frac{\\sqrt[3]{ 21}}{-4ab\u00b2}\\)<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 37 and 38, describe and correct the error in simplifying the expression.<br \/>\nQuestion 37.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35272\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 3\" width=\"259\" height=\"105\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41955\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-37.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 37\" width=\"578\" height=\"161\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-37.png 578w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-37-300x84.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 38.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35273\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-4.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 4\" width=\"335\" height=\"192\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-4.png 335w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-4-300x172.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><br \/>\nAnswer:<br \/>\n\\(\\sqrt[3]{\\frac{128 y^{3}}{125}}\\)<br \/>\n= \\(\\frac{\\sqrt[3]{128 y^{3}}}{\\sqrt[3]{125}}\\)<br \/>\n= \\(\\frac{\\sqrt[3]{64 y^{3} \u00d7 2}}{\\sqrt[3]{125}}\\)<br \/>\n= \\(\\frac{4y\\sqrt[3]{ 2}}{5}\\)<\/p>\n<p><strong>In Exercises 39\u201344, write a factor that you can use to rationalize the denominator of the expression.<\/strong><br \/>\nQuestion 39.<br \/>\n\\(\\frac{4}{\\sqrt{6}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41956\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-39.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 39\" width=\"494\" height=\"109\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-39.png 494w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-39-300x66.png 300w\" sizes=\"(max-width: 494px) 100vw, 494px\" \/><\/p>\n<p>Question 40.<br \/>\n\\(\\frac{1}{\\sqrt{13 z}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{\\sqrt{13 z}}\\)<br \/>\nTo rationalize the given expression,<br \/>\nWe have to multiply the given expression by a factor \\(\\frac{\\sqrt{13 z}}{\\sqrt{13 z}}\\)<\/p>\n<p>Question 41.<br \/>\n\\(\\frac{2}{\\sqrt[3]{x^{2}}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41957\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-41.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 41\" width=\"524\" height=\"112\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-41.png 524w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-41-300x64.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><\/p>\n<p>Question 42.<br \/>\n\\(\\frac{3 m}{\\sqrt[3]{4}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{3 m}{\\sqrt[3]{4}}\\)<br \/>\nWe have to multiply the given expression by a factor \\(\\frac{\\sqrt[3]{2}}{\\sqrt[3]{2}}\\)<\/p>\n<p>Question 43.<br \/>\n\\(\\frac{\\sqrt{2}}{\\sqrt{5}-8}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41958\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-43.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 43\" width=\"528\" height=\"117\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-43.png 528w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-43-300x66.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p>Question 44.<br \/>\n\\(\\frac{5}{\\sqrt{3}+\\sqrt{7}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{5}{\\sqrt{3}+\\sqrt{7}}\\)<br \/>\nWe have to multiply the given expression by a factor \\(\\frac{\\sqrt{3} &#8211; \\sqrt{7}}{\\sqrt{3} &#8211; \\sqrt{7}}\\)<\/p>\n<p><strong>In Exercises 45\u201354, simplify the expression.<\/strong><br \/>\nQuestion 45.<br \/>\n\\(\\frac{2}{\\sqrt{2}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41959\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-45.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 45\" width=\"153\" height=\"246\" \/><\/p>\n<p>Question 46.<br \/>\n\\(\\frac{4}{\\sqrt{3}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{4}{\\sqrt{3}}\\)<br \/>\n= \\(\\frac{4}{\\sqrt{3}}\\) \u00d7 (\\(\\sqrt{3}\\) \/ \\(\\sqrt{3}\\))<br \/>\n= 4\\(\\sqrt{3}\\) \/ (\\(\\sqrt{3}\\) \u00d7 \\(\\sqrt{3}\\))<br \/>\n= 4\\(\\sqrt{3}\\) \/ 3<\/p>\n<p>Question 47.<br \/>\n\\(\\frac{\\sqrt{5}}{\\sqrt{48}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41960\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-47.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 47\" width=\"190\" height=\"485\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-47.png 190w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-47-118x300.png 118w\" sizes=\"(max-width: 190px) 100vw, 190px\" \/><\/p>\n<p>Question 48.<br \/>\n\\(\\sqrt{\\frac{4}{52}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{\\frac{4}{52}}\\)<br \/>\n= \\(\\frac{\\sqrt{4}}{\\sqrt{52}}\\)<br \/>\n= \\(\\frac{\\sqrt{4}}{\\sqrt{4 \u00d7 13}}\\)<br \/>\n= \\(\\frac{2}{2\\sqrt{13}}\\)<\/p>\n<p>Question 49.<br \/>\n\\(\\frac{3}{\\sqrt{a}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41961\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-49.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 49\" width=\"150\" height=\"183\" \/><\/p>\n<p>Question 50.<br \/>\n\\(\\frac{1}{\\sqrt{2 x}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{\\sqrt{2 x}}\\)<br \/>\n= \\(\\frac{1}{\\sqrt{2 x}}\\) \u00d7 (\\(\\sqrt{2 x}\\) \/ \\(\\sqrt{2 x}\\))<br \/>\n= \\(\\sqrt{2 x}\\) \/ (\\(\\sqrt{2 x}\\) \u00d7 \\(\\sqrt{2 x}\\))<br \/>\n= \\(\\sqrt{2 x}\\) \/ 2x<\/p>\n<p>Question 51.<br \/>\n\\(\\sqrt{\\frac{3 d^{2}}{5}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41962\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-51.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 51\" width=\"198\" height=\"340\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-51.png 198w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-51-175x300.png 175w\" sizes=\"(max-width: 198px) 100vw, 198px\" \/><\/p>\n<p>Question 52.<br \/>\n\\(\\frac{\\sqrt{8}}{\\sqrt{3 n^{3}}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{\\sqrt{8}}{\\sqrt{3 n^{3}}}\\)<br \/>\n= \\(\\frac{\\sqrt{4 \u00d7 2}}{\\sqrt{3 n^{2} \u00d7 n}}\\)<br \/>\n= \\(\\frac{2\\sqrt{2}}{n\\sqrt{3 n}}\\)<\/p>\n<p>Question 53.<br \/>\n\\(\\frac{4}{\\sqrt[3]{25}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41963\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-53.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 53\" width=\"184\" height=\"213\" \/><\/p>\n<p>Question 54.<br \/>\n\\(\\sqrt[3]{\\frac{1}{108 y^{2}}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt[3]{\\frac{1}{108 y^{2}}}\\)<br \/>\n= \\(\\frac{\\sqrt[3]{1}}{\\sqrt[3]{27 \u00d7 4 y^{2}}}\\)<br \/>\n= \\(\\frac{2\\sqrt[3]{1}}{3\\sqrt[3]{4 y^{2}}}\\)<br \/>\n\\(\\sqrt[3]{\\frac{1}{108 y^{2}}}\\) = \\(\\frac{2\\sqrt[3]{1}}{3\\sqrt[3]{4 y^{2}}}\\)<\/p>\n<p><strong>In Exercises 55\u201360, simplify the expression.<\/strong><br \/>\nQuestion 55.<br \/>\n\\(\\frac{1}{\\sqrt{7}+1}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41964\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-55.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 55\" width=\"275\" height=\"268\" \/><\/p>\n<p>Question 56.<br \/>\n\\(\\frac{2}{5-\\sqrt{3}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{2}{5 &#8211; \\sqrt{3}}\\)<br \/>\n= \\(\\frac{2}{5 &#8211; \\sqrt{3}}\\) \u00d7 (\\(5 + \\sqrt{3}\\) \/ \\(5 + \\sqrt{3}\\))<br \/>\n= 2\\((5 + \\sqrt{3})\\) \/ (\\(5 + \\sqrt{3}\\) \u00d7 \\(5 &#8211; \\sqrt{3}\\))<br \/>\n= 2\\((5 + \\sqrt{3})\\) \/ 22<br \/>\n= \\((5 + \\sqrt{3})\\) \/ 11<\/p>\n<p>Question 57.<br \/>\n\\(\\frac{\\sqrt{10}}{7-\\sqrt{2}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41965\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-57.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 57\" width=\"308\" height=\"388\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-57.png 308w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-57-238x300.png 238w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><\/p>\n<p>Question 58.<br \/>\n\\(\\frac{\\sqrt{5}}{6+\\sqrt{5}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{\\sqrt{5}}{6 + \\sqrt{5}}\\)<br \/>\n= \\(\\frac{\\sqrt{5}}{6 + \\sqrt{5}}\\) \u00d7 (\\( 6 &#8211; \\sqrt{5} \\) \/ \\(6 &#8211; \\sqrt{5}\\))<br \/>\n= \\(\\frac{\\sqrt{5}}{6 &#8211; \\sqrt{5}}\\) \/ (\\(6 +\u00a0 \\sqrt{5} \\) \u00d7 \\( 6 &#8211; \\sqrt{5} \\))<br \/>\n= \\(\\frac{\\sqrt{5}}{6 + \\sqrt{5}}\\) \/ 31<\/p>\n<p>Question 59.<br \/>\n\\(\\frac{3}{\\sqrt{5}-\\sqrt{2}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41966\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-59.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 59\" width=\"320\" height=\"295\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-59.png 320w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-59-300x277.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><\/p>\n<p>Question 60.<br \/>\n\\(\\frac{\\sqrt{3}}{\\sqrt{7}+\\sqrt{3}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{\\sqrt{3}}{\\sqrt{7}+\\sqrt{3}}\\)<br \/>\n= \\(\\frac{\\sqrt{3}}{\\sqrt{7}+\\sqrt{3}}\\) \u00d7 (\\(\\sqrt{7} -\\sqrt{3} \\) \/ \\(\\sqrt{7} -\\sqrt{3} \\))<br \/>\n= \\(\\frac{\\sqrt{3}}{\\sqrt{7}-\\sqrt{3}}\\) \/ (\\(\\sqrt{7} +\\sqrt{3} \\) \u00d7 \\(\\sqrt{7} -\\sqrt{3} \\))<br \/>\n= \\(\\frac{\\sqrt{3}}{\\sqrt{7}+\\sqrt{3}}\\) \/ 4<\/p>\n<p>Question 61.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe time t (in seconds) it takes an object to hit the ground is given by t = \\(\\sqrt{\\frac{h}{16}}\\), where his the height (in feet) from which the object was dropped.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35274\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 5\" width=\"148\" height=\"167\" \/><br \/>\na. How long does it take an earring to hit the ground when it falls from the roof of the building?<br \/>\nb. How much sooner does the earring hit the ground when it is dropped from two stories (22 feet) below the roof?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41967\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-61.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 61\" width=\"567\" height=\"346\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-61.png 567w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-61-300x183.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 62.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe orbital period of a planet is the time it takes the planet to travel around the Sun. You can find the orbital period P (in Earth years) using the formula P = \\(\\sqrt{d^{3}}\\), where d is the average distance (in astronomical units, abbreviated AU) of the planet from the Sun.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35275\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-6.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 6\" width=\"311\" height=\"143\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-6.png 311w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-6-300x138.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><br \/>\na. Simplify the formula.<br \/>\nAnswer:<br \/>\nP = \\(\\sqrt{d^{3}}\\)<br \/>\nwhere d is the average distance<br \/>\nP = \\(\\sqrt{d^{3}}\\)<br \/>\nP = \\(\\sqrt{d^{2} \u00d7 d}\\)<br \/>\nP = d\\(\\sqrt{d}\\)<\/p>\n<p>b. What is Jupiter\u2019s orbital period?<br \/>\nAnswer:<br \/>\nP = d\\(\\sqrt{d}\\)<br \/>\nThe distance of Jupiter from the sun is: 5.2 AU<br \/>\nThe Orbital Period of Jupiter (P) is:<br \/>\nP = \\(\\sqrt{5.2^{3}}\\)<br \/>\nP = 11.85 AU<\/p>\n<p>Question 63.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe electric current I (in amperes) an appliance uses is given by the formula I = \\(\\sqrt{\\frac{P}{R}}\\), where P is the power (in watts) and R is the resistance (in ohms). Find the current an appliance uses when the power is 147 watts and the resistance is 5 ohms.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35276\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 7\" width=\"249\" height=\"190\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41968\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-63.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 63\" width=\"573\" height=\"483\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-63.png 573w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-63-300x253.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 64.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou can find the average annual interest rate r (in decimal form) of a savings account using the formula r = \\(\\sqrt{\\frac{V_{2}}{V_{0}}}\\) &#8211; 1, where V<sub>0<\/sub> is the initial investment and V<sub>2<\/sub> is the balance of the account after 2 years. Use the formula to compare the savings accounts. In which account would you invest money? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35277\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-8.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 8\" width=\"300\" height=\"177\" \/><br \/>\nAnswer:<br \/>\nr = \\(\\sqrt{\\frac{V_{2}}{V_{0}}}\\) &#8211; 1<br \/>\nwhere,<br \/>\nV<sub>0<\/sub> is the initial investment<br \/>\nV<sub>2<\/sub> is the balance of the account after 2 years<br \/>\nFor \\(\\frac{V_{2}}{V_{0}}\\) = \\(\\frac{293}{275}\\),<br \/>\nr = \\(\\sqrt{\\frac{293}{275}}\\) &#8211; 1<br \/>\nr = 3.19%<br \/>\nFor \\(\\frac{V_{2}}{V_{0}}\\) = \\(\\frac{382}{361}\\),<br \/>\nr = \\(\\sqrt{\\frac{382}{361}}\\) &#8211; 1<br \/>\nr = 2.85%<br \/>\nFor \\(\\frac{V_{2}}{V_{0}}\\) = \\(\\frac{214}{199}\\),<br \/>\nr = \\(\\sqrt{\\frac{214}{199}}\\) &#8211; 1<br \/>\nr = 3.68%<br \/>\nFor \\(\\frac{V_{2}}{V_{0}}\\) = \\(\\frac{272}{254}\\),<br \/>\nr = \\(\\sqrt{\\frac{272}{254}}\\) &#8211; 1<br \/>\nr = 3.44%<br \/>\nFor \\(\\frac{V_{2}}{V_{0}}\\) = \\(\\frac{406}{386}\\),<br \/>\nr = \\(\\sqrt{\\frac{406}{386}}\\) &#8211; 1<br \/>\nr = 2.51%<\/p>\n<p><strong>In Exercises 65\u201368, evaluate the function for the given value of x. Write your answer in simplest form and in decimal form rounded to the nearest hundredth.<\/strong><br \/>\nQuestion 65.<br \/>\nh(x) = \\(\\sqrt{5x}\\); x = 10<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41969\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-65.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 65\" width=\"303\" height=\"246\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-65.png 303w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-65-300x244.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><\/p>\n<p>Question 66.<br \/>\ng(x) = \\(\\sqrt{3x}\\); x = 60<br \/>\nAnswer:<br \/>\ng(x) = \\(\\sqrt{3x}\\)<br \/>\nx = 60<br \/>\ng(60) = \\(\\sqrt{3 \u00d7 60}\\)<br \/>\ng(60) = \\(\\sqrt{9 \u00d7 20}\\)<br \/>\ng(60) = \\(\\sqrt{9 \u00d7 5 \u00d7 4}\\)<br \/>\ng(60) = \\(\\sqrt{36 \u00d7 5}\\)<br \/>\ng(60) = 6\\(\\sqrt{5}\\)<br \/>\ng(60) = 13.41<\/p>\n<p>Question 67.<br \/>\nr(x) = \\(\\sqrt{\\frac{3 x}{3 x^{2}+6}}\\); x = 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41970\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-67.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 67\" width=\"302\" height=\"566\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-67.png 302w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-67-160x300.png 160w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><\/p>\n<p>Question 68.<br \/>\np(x) = \\(\\sqrt{\\frac{x-1}{5 x}}\\); x = 8<br \/>\nAnswer:<br \/>\np(x) = \\(\\sqrt{\\frac{x-1}{5 x}}\\) with x = 8<br \/>\np(8) = \\(\\sqrt{\\frac{8-1}{5 \u00d7 8}}\\)<br \/>\np(8) = \\(\\sqrt{\\frac{7}{40}}\\)<br \/>\np(8) = 0.41<\/p>\n<p><strong>In Exercises 69\u201372, evaluate the expression when a = \u22122, b = 8, and c = \\(\\frac{1}{2}\\). Write your answer in simplest form and in decimal form rounded to the nearest hundredth.<\/strong><br \/>\nQuestion 69.<br \/>\n\\(\\sqrt{a^{2}+b c}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41971\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-69.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 69\" width=\"305\" height=\"216\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-69.png 305w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-69-300x212.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Question 70.<br \/>\n\\(-\\sqrt{4 c-6 a b}\\)<br \/>\nAnswer:<br \/>\n\\(-\\sqrt{4 c-6 a b}\\)<br \/>\n= \\(-\\sqrt{4 \u00d7 (1\/2) &#8211; 6 (-2) (8)}\\)<br \/>\n= \\(-\\sqrt{2- 6 (-16)}\\)<br \/>\n= \\(-\\sqrt{2 + 96}\\)<br \/>\n= \\(-\\sqrt{98}\\)<br \/>\n= -9.89<\/p>\n<p>Question 71.<br \/>\n\\(-\\sqrt{2 a^{2}+b^{2}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41972\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-71.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 71\" width=\"371\" height=\"243\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-71.png 371w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-71-300x196.png 300w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><\/p>\n<p>Question 72.<br \/>\n\\(\\sqrt{b^{2}-4 a c}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{b^{2}-4 a c}\\)<br \/>\n= \\(\\sqrt{8^{2}-4 (-2) \u00d7 (1\/2)}\\)<br \/>\n= \\(\\sqrt{64 + 4}\\)<br \/>\n= \\(\\sqrt{68}\\)<br \/>\n= 8.24<\/p>\n<p>Question 73.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe text in the book shown forms a golden rectangle. What is the width w of the text?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35278\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 9\" width=\"259\" height=\"182\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41973\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-73.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 73\" width=\"400\" height=\"617\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-73.png 400w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-73-194x300.png 194w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>Question 74.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe flag of Togo is approximately the shape of a golden rectangle. What is the width w of the flag?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35279\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-10.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 10\" width=\"293\" height=\"172\" \/><br \/>\nAnswer:<br \/>\nThe flag of Togo is approximately the shape of a golden rectangle<br \/>\nThe length of the golden rectangle is 42 in.<br \/>\nThe width of the given rectangle is w inch<br \/>\nThe ratio of the length and the width in a golden rectangle = \\(\\frac{1+\\sqrt{5}}{2}\\)<br \/>\n\\(\\frac{1+\\sqrt{5}}{2}\\) = \\(\\frac{42}{w}\\)<br \/>\nw (\\(1 + \\sqrt{5}\\)) = 42 \u00d7 2<br \/>\nh (\\(1 + \\sqrt{5}\\)) = 84<br \/>\nh = \\(\\frac{84}{1 + \\sqrt{5}}\\)<br \/>\n\\(\\frac{84}{1 + \\sqrt{5}}\\)<br \/>\n= \\(\\frac{84}{1 + \\sqrt{5}}\\) \u00d7 (\\(1 &#8211; \\sqrt{5}\\) \/ \\(1 &#8211; \\sqrt{5}\\))<br \/>\n= 84\\((1 &#8211; \\sqrt{5})\\) \/ (\\(1 + \\sqrt{5}\\) \u00d7 \\(1 &#8211; \\sqrt{5}\\))<br \/>\n= 84\\((1 &#8211; \\sqrt{5})\\) \/ -4<br \/>\n= &#8211; 84\\((1 &#8211; \\sqrt{5})\\) \/ 4<br \/>\n= 25.95 in<br \/>\nHence, from the above,<\/p>\n<p><strong>In Exercises 75\u201382, simplify the expression.<\/strong><br \/>\nQuestion 75.<br \/>\n\\(\\sqrt{2}\\) &#8211; 2\\(\\sqrt{2}\\) + 6\\(\\sqrt{2}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41974\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-75.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 75\" width=\"379\" height=\"67\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-75.png 379w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-75-300x53.png 300w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><\/p>\n<p>Question 76.<br \/>\n\\(\\sqrt{5}\\) &#8211; 5\\(\\sqrt{13}\\) &#8211; 8\\(\\sqrt{5}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{5}\\) &#8211; 5\\(\\sqrt{13}\\) &#8211; 8\\(\\sqrt{5}\\)<br \/>\n= \\(\\sqrt{5}\\) (1 &#8211; 8) &#8211; 5\\(\\sqrt{13}\\)<br \/>\n= \\(\\sqrt{5}\\) (-7) &#8211; 5\\(\\sqrt{13}\\)<br \/>\n= -7\\(\\sqrt{5}\\)\u00a0 &#8211; 5\\(\\sqrt{13}\\)<\/p>\n<p>Question 77.<br \/>\n2\\(\\sqrt{6}\\) &#8211; 5\\(\\sqrt{54}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41975\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-77.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 77\" width=\"339\" height=\"207\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-77.png 339w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-77-300x183.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/p>\n<p>Question 78.<br \/>\n9\\(\\sqrt{32}\\) + \\(\\sqrt{2}\\)<br \/>\nAnswer:<br \/>\n9\\(\\sqrt{32}\\) + \\(\\sqrt{2}\\)<br \/>\n= 9\\(\\sqrt{16 \u00d7 2}\\) + \\(\\sqrt{2}\\)<br \/>\n= 9 (4)\\(\\sqrt{2}\\) + \\(\\sqrt{2}\\)<br \/>\n= 36\\(\\sqrt{2}\\) + \\(\\sqrt{2}\\)<br \/>\n= \\(\\sqrt{2}\\) (6 + 1)<br \/>\n= \\(\\sqrt{2}\\) (7)<br \/>\n= 7\\(\\sqrt{2}\\)<\/p>\n<p>Question 79.<br \/>\n\\(\\sqrt{12}\\) + 6\\(\\sqrt{3}\\) + 2\\(\\sqrt{6}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41976\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-79.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 79\" width=\"431\" height=\"170\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-79.png 431w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-79-300x118.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/p>\n<p>Question 80.<br \/>\n3\\(\\sqrt{7}\\) &#8211; 5\\(\\sqrt{14}\\) + 2\\(\\sqrt{28}\\)<br \/>\nAnswer:<br \/>\n3\\(\\sqrt{7}\\) &#8211; 5\\(\\sqrt{14}\\) + 2\\(\\sqrt{28}\\)<br \/>\n= 3\\(\\sqrt{7}\\) &#8211; 5\\(\\sqrt{14}\\) + 2\\(\\sqrt{7 \u00d7 4}\\)<br \/>\n= 3\\(\\sqrt{7}\\) &#8211; 5\\(\\sqrt{14}\\) + 2 (2)\\(\\sqrt{7}\\)<br \/>\n= 3\\(\\sqrt{7}\\) &#8211; 5\\(\\sqrt{14}\\) + 4\\(\\sqrt{7}\\)<br \/>\n= \\(\\sqrt{7}\\) (3 + 4) &#8211; 5\\(\\sqrt{14}\\)<br \/>\n= \\(\\sqrt{7}\\) (7) &#8211; 5\\(\\sqrt{14}\\)<br \/>\n= 7\\(\\sqrt{7}\\) &#8211; 5\\(\\sqrt{14}\\)<\/p>\n<p>Question 81.<br \/>\n\\(\\sqrt[3]{-81}\\) + 4\\(\\sqrt[3]{3}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41977\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-81.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 81\" width=\"363\" height=\"218\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-81.png 363w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-81-300x180.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 82.<br \/>\n6\\(\\sqrt[3]{128 t}\\) &#8211; 2\\(\\sqrt[3]{2 t}\\)<br \/>\nAnswer:<br \/>\n6\\(\\sqrt[3]{128 t}\\) &#8211; 2\\(\\sqrt[3]{2 t}\\)<br \/>\n= 6\\(\\sqrt[3]{64 \u00d7 2 t}\\) &#8211; 2\\(\\sqrt[3]{2 t}\\)<br \/>\n= 6 (4)\\(\\sqrt[3]{2 t}\\) &#8211; 2\\(\\sqrt[3]{2 t}\\)<br \/>\n= 24\\(\\sqrt[3]{2 t}\\) &#8211; 2\\(\\sqrt[3]{2 t}\\)<br \/>\n= \\(\\sqrt[3]{2 t}\\) (24 &#8211; 2)<br \/>\n= \\(\\sqrt[3]{2 t}\\) (22)<br \/>\n= 22\\(\\sqrt[3]{2 t}\\)<\/p>\n<p><strong>In Exercises 83\u201390, simplify the expression.<\/strong><br \/>\nQuestion 83.<br \/>\n\\(\\sqrt{2}\\)(\\(\\sqrt{45}\\) + \\(\\sqrt{5}\\))<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41978\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-83.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 83\" width=\"390\" height=\"248\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-83.png 390w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-83-300x191.png 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><\/p>\n<p>Question 84.<br \/>\n\\(\\sqrt{3}\\)(\\(\\sqrt{72}\\) &#8211; 3\\(\\sqrt{2}\\))<br \/>\nAnswer:<br \/>\n\\(\\sqrt{3}\\)(\\(\\sqrt{72}\\) &#8211; 3\\(\\sqrt{2}\\))<br \/>\n= \\(\\sqrt{3}\\)(\\(\\sqrt{36 \u00d7 2}\\) &#8211; 3\\(\\sqrt{2}\\))<br \/>\n= \\(\\sqrt{3}\\)(6\\(\\sqrt{2}\\) &#8211; 3\\(\\sqrt{2}\\))<br \/>\n= \\(\\sqrt{3}\\)(\\(\\sqrt{2}\\) (6 &#8211; 3))<br \/>\n= \\(\\sqrt{3}\\)(\\(\\sqrt{2}\\) (3))<br \/>\n= \\(\\sqrt{3}\\)(3\\(\\sqrt{2}\\))<br \/>\n= 3 \u00d7\u00a0 \\(\\sqrt{3}\\) \u00d7 \\(\\sqrt{2}\\)<br \/>\n= 3 \\(\\sqrt{6}\\)<\/p>\n<p>Question 85.<br \/>\n\\(\\sqrt{5}\\)(2\\(\\sqrt{6x}\\) &#8211; \\(\\sqrt{96x}\\))<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41979\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-85.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 85\" width=\"449\" height=\"246\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-85.png 449w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-85-300x164.png 300w\" sizes=\"(max-width: 449px) 100vw, 449px\" \/><\/p>\n<p>Question 86.<br \/>\n\\(\\sqrt{7y}\\)(\\(\\sqrt{27y}\\) + 5\\(\\sqrt{12y}\\))<br \/>\nAnswer:<br \/>\n\\(\\sqrt{7y}\\)(\\(\\sqrt{27y}\\) + 5\\(\\sqrt{12y}\\))<br \/>\n= \\(\\sqrt{7y}\\)(\\(\\sqrt{9 \u00d7 3y}\\) + 5\\(\\sqrt{4 \u00d7 3y}\\))<br \/>\n= \\(\\sqrt{7y}\\)(3\\(\\sqrt{3y}\\) + 5 (2)\\(\\sqrt{3y}\\))<br \/>\n= \\(\\sqrt{7y}\\)(3\\(\\sqrt{3y}\\) + 10\\(\\sqrt{3y}\\))<br \/>\n= \\(\\sqrt{7y}\\)(\\(\\sqrt{3y}\\) (3 + 10))<br \/>\n= \\(\\sqrt{7y}\\)(\\(\\sqrt{3y}\\) (13))<br \/>\n= 13 \u00d7 \\(\\sqrt{7y}\\) \u00d7 \\(\\sqrt{3y}\\)<br \/>\n= 13(\\(\\sqrt{21y}\\)<\/p>\n<p>Question 87.<br \/>\n(4\\(\\sqrt{2}\\) &#8211; \\(\\sqrt{98}\\))<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41980\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-87.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 87\" width=\"498\" height=\"209\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-87.png 498w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-87-300x126.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><\/p>\n<p>Question 88.<br \/>\n(\\(\\sqrt{3}\\) + \\(\\sqrt{48}\\)) (\\(\\sqrt{20}\\) &#8211; \\(\\sqrt{5}\\))<br \/>\nAnswer:<br \/>\n(\\(\\sqrt{3}\\) + \\(\\sqrt{48}\\)) (\\(\\sqrt{20}\\) &#8211; \\(\\sqrt{5}\\))<br \/>\n= (\\(\\sqrt{3}\\) + \\(\\sqrt{16 \u00d7 3}\\)) (\\(\\sqrt{5 \u00d7 4}\\) &#8211; \\(\\sqrt{5}\\))<br \/>\n= (\\(\\sqrt{3}\\) + 4\\(\\sqrt{3}\\)) (2\\(\\sqrt{5}\\) &#8211; \\(\\sqrt{5}\\))<br \/>\n= (\\(\\sqrt{3}\\) (1 + 4)) (\\(\\sqrt{5}\\) (2 &#8211; 1))<br \/>\n= (\\(\\sqrt{3}\\) (5)) (\\(\\sqrt{5}\\) (1))<br \/>\n= 5\\(\\sqrt{3}\\) \u00d7 \\(\\sqrt{5}\\)<br \/>\n= 5\\(\\sqrt{15}\\)<\/p>\n<p>Question 89.<br \/>\n\\(\\sqrt[3]{3}(\\sqrt[3]{4}+\\sqrt[3]{32})\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41981\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-89.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 89\" width=\"422\" height=\"250\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-89.png 422w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-89-300x178.png 300w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><\/p>\n<p>Question 90.<br \/>\n\\(\\sqrt[3]{2}(\\sqrt[3]{135}-4 \\sqrt[3]{5})\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt[3]{2}(\\sqrt[3]{135}-4 \\sqrt[3]{5})\\)<br \/>\n= \\(\\sqrt[3]{2}(\\sqrt[3]{5 \u00d7 27}-4 \\sqrt[3]{5})\\)<br \/>\n= \\(\\sqrt[3]{2}(3\\sqrt[3]{5}-4 \\sqrt[3]{5})\\)<br \/>\n= \\(\\sqrt[3]{2}(\\sqrt[3]{5} (3 &#8211; 4)\\)<br \/>\n= \\(\\sqrt[3]{2}(\\sqrt[3]{5} (-1)\\)<br \/>\n= &#8211;\\(\\sqrt[3]{2}(\\sqrt[3]{5}) \\)<br \/>\n= &#8211;\\(\\sqrt[3]{10}\\)<\/p>\n<p>Question 91.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe circumference C of the art room in a mansion is approximated by the formula C \u2248 \\(\\sqrt\\frac{a^{2}+b^{2}}{2}\\). Approximate the circumference of the room.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35280\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 11\" width=\"324\" height=\"327\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-11.png 324w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-11-297x300.png 297w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-11-150x150.png 150w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41982\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-91.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 91\" width=\"528\" height=\"481\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-91.png 528w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-91-300x273.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p>Question 92.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nDetermine whether each expression represents a rational or an irrational number. Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35281\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-12.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 12\" width=\"303\" height=\"192\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-12.png 303w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-12-300x190.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><br \/>\nAnswer:<br \/>\na.<br \/>\n4 + \\(\\sqrt{6}\\)<br \/>\nAny fraction that we can write in the form of \\(\\frac{p}{q}\\) is called a &#8220;Rational Number&#8221;. Otherwise, that number is an &#8220;Irrational number&#8221;<br \/>\nWe can say that the given expression can&#8217;t be expressed in the form of \\(\\frac{p}{q}\\)<br \/>\nWe can conclude that 4 + \\(\\sqrt{6}\\) is an irrational number<br \/>\nb.<br \/>\n\\(\\frac{\\sqrt{48}}{\\sqrt{3}}\\)<br \/>\nAny fraction that we can write in the form of \\(\\frac{p}{q}\\) is called a &#8220;Rational Number&#8221;. Otherwise, that number is an &#8220;Irrational number&#8221;<br \/>\nWe can say that the given expression can be expressed in the form of \\(\\frac{p}{q}\\)<br \/>\nWe can conclude that \\(\\frac{\\sqrt{48}}{\\sqrt{3}}\\) is a rational number<br \/>\nc.<br \/>\n\\(\\frac{8}{\\sqrt{12}}\\)<br \/>\nAny fraction that we can write in the form of \\(\\frac{p}{q}\\) is called a &#8220;Rational Number&#8221;. Otherwise, that number is an &#8220;Irrational number&#8221;<br \/>\nWe can say that the given expression can&#8217;t be expressed in the form of \\(\\frac{p}{q}\\)<br \/>\nWe can conclude that \\(\\frac{8}{\\sqrt{12}}\\) is an irrational number<br \/>\nd.<br \/>\n\\(\\frac{\\sqrt{3}}{\\sqrt{7}}\\)<br \/>\nAny fraction that we can write in the form of \\(\\frac{p}{q}\\) is called a &#8220;Rational Number&#8221;. Otherwise, that number is an &#8220;Irrational number&#8221;<br \/>\nWe can say that the given expression can&#8217;t be expressed in the form of \\(\\frac{p}{q}\\)<br \/>\nWe can conclude that\\(\\frac{\\sqrt{3}}{\\sqrt{7}}\\) is an irrational number<br \/>\ne.<br \/>\n\\(\\frac{a}{\\sqrt{10} &#8211; \\sqrt{2}}\\)<br \/>\nAny fraction that we can write in the form of \\(\\frac{p}{q}\\) is called a &#8220;Rational Number&#8221;. Otherwise, that number is an &#8220;Irrational number&#8221;<br \/>\nWe can say that the given expression can be expressed in the form of \\(\\frac{p}{q}\\)<br \/>\nWe can conclude that\\(\\frac{a}{\\sqrt{10} &#8211; \\sqrt{2}}\\) is a rational number<br \/>\nf.<br \/>\n\\(\\frac{2 + \\sqrt{5}}{2 b + \\sqrt{5 b^{2}}}\\)<br \/>\nAny fraction that we can write in the form of \\(\\frac{p}{q}\\) is called a &#8220;Rational Number&#8221;. Otherwise, that number is an &#8220;Irrational number&#8221;<br \/>\nWe can say that the given expression can be expressed in the form of \\(\\frac{p}{q}\\)<br \/>\nWe can conclude that\\(\\frac{2 + \\sqrt{5}}{2 b + \\sqrt{5 b^{2}}}\\) is a rational number<\/p>\n<p><strong>In Exercises 93\u201398, simplify the expression.<\/strong><br \/>\nQuestion 93.<br \/>\n\\(\\sqrt[5]{\\frac{13}{5 x^{5}}}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41983\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-93.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 93\" width=\"227\" height=\"546\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-93.png 227w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-93-125x300.png 125w\" sizes=\"(max-width: 227px) 100vw, 227px\" \/><\/p>\n<p>Question 94.<br \/>\n\\(\\sqrt[4]{\\frac{10}{81}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt[4]{\\frac{10}{81}}\\)<br \/>\n= \\(\\frac{\\sqrt[4]{10}}{\\sqrt[4]{81}}\\)<br \/>\n= \\(\\frac{\\sqrt[4]{10}}{\\sqrt[4]{3^{4}}}\\)<br \/>\n= \\(\\frac{\\sqrt[4]{10}}{3}\\)<\/p>\n<p>Question 95.<br \/>\n\\(\\sqrt[4]{256 y}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41984\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-95.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 95\" width=\"299\" height=\"42\" \/><\/p>\n<p>Question 96.<br \/>\n\\(\\sqrt[5]{160 x^{6}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt[5]{160 x^{6}}\\)<br \/>\n= \\(\\sqrt[5]{40 (4) x^{5} \u00d7 x}\\)<br \/>\n= \\(\\sqrt[5]{20 (8) x^{5} \u00d7 x}\\)<br \/>\n= \\(\\sqrt[5]{32 (5) x^{5} \u00d7 x}\\)<br \/>\n= \\(\\sqrt[5]{2^{5} \u00d7 5\u00a0 x^{5} \u00d7 x}\\)<br \/>\n= 2x\\(\\sqrt[5]{5 x}\\)<\/p>\n<p>Question 97.<br \/>\n\\(6 \\sqrt[4]{9}-\\sqrt[5]{9}+3 \\sqrt[4]{9}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41985\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-97.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 97\" width=\"406\" height=\"109\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-97.png 406w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-97-300x81.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/p>\n<p>Question 98.<br \/>\n\\(\\sqrt[5]{2}(\\sqrt[4]{7}+\\sqrt[5]{16})\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt[5]{2}(\\sqrt[4]{7}+\\sqrt[5]{16})\\)<br \/>\n= (\\(\\sqrt[5]{2}\\) \u00d7 \\(\\sqrt[4]{7}\\)) + (\\(\\sqrt[5]{2}\\) \u00d7 \\(\\sqrt[5]{16}\\))<br \/>\n= (\\(\\sqrt[5]{2}\\) \u00d7 \\(\\sqrt[4]{7}\\)) + (\\(\\sqrt[5]{32}\\)<br \/>\n= (\\(\\sqrt[5]{2}\\) \u00d7 \\(\\sqrt[4]{7}\\)) + 2<\/p>\n<p><strong>REASONING<\/strong> In Exercises 99 and 100, use the table shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35282\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 13\" width=\"321\" height=\"213\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-13.png 321w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-13-300x199.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nQuestion 99.<br \/>\nCopy and complete the table by (a) finding each sum ( 2 + 2, 2 + \\(\\frac{1}{4}\\), etc. ) and (b) finding each product ( 2 \u2022 2, 2 \u2022 \\(\\frac{1}{4}\\), etc. )<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41986\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 99.1\" width=\"599\" height=\"356\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.1.png 599w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.1-300x178.png 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41987\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 99.2\" width=\"550\" height=\"330\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.2.png 550w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.2-300x180.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 100.<br \/>\nUse your answers in Exercise 99 to determine whether each statement is always, sometimes, or never true. Justify your answer.<br \/>\na. The sum of a rational number and a rational number is rational.<br \/>\nb. The sum of a rational number and an irrational number is irrational.<br \/>\nc. The sum of an irrational number and an irrational number is irrational.<br \/>\nd. The product of a rational number and a rational number is rational.<br \/>\ne. The product of a nonzero rational number and an irrational number is irrational.<br \/>\nf. The product of an irrational number and an irrational number is irrational.<br \/>\nAnswer:<br \/>\nFrom Exercise 99,<br \/>\na. The completed table of the sum of rational numbers and irrational numbers is:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41986\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 99.1\" width=\"599\" height=\"356\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.1.png 599w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.1-300x178.png 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><br \/>\nb. The completed table of the product of rational numbers and irrational numbers is:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41987\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 99.2\" width=\"550\" height=\"330\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.2.png 550w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.2-300x180.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><br \/>\nThe given statements are:<br \/>\na. The sum of a rational number and a rational number is rational.<br \/>\nb. The sum of a rational number and an irrational number is irrational.<br \/>\nc. The sum of an irrational number and an irrational number is irrational.<br \/>\nd. The product of a rational number and a rational number is rational.<br \/>\ne. The product of a nonzero rational number and an irrational number is irrational.<br \/>\nf. The product of an irrational number and an irrational number is irrational.<br \/>\nSo,<br \/>\na.<br \/>\nThe given statement is sometimes true<br \/>\nb.<br \/>\nThe given statement is sometimes true<br \/>\nc.<br \/>\nThe given statement is always true<br \/>\nd.<br \/>\nThe given statement is always true<br \/>\ne.<br \/>\nThe given statement is sometimes true<br \/>\nf.<br \/>\nThe given statement is sometimes true<\/p>\n<p>Question 101.<br \/>\n<strong>REASONING<\/strong><br \/>\nLet m be a positive integer. For what values of m will the simplified form of the expression \\(\\sqrt{2^{m}}\\) contain a radical? For what values will it not contain a radical? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41988\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-101.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 101\" width=\"572\" height=\"144\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-101.png 572w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-101-300x76.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 102.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe edge length s of a cube is an irrational number, a surface area is an irrational number, and a volume is a rational number. Give a possible value of s.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35283\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-14.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 14\" width=\"149\" height=\"117\" \/><br \/>\nAnswer:<br \/>\nThe length (s) of a cube is: An irrational number<br \/>\nThe surface area of a cube is: An irrational number<br \/>\nThe volume of a cube is: A rational number<br \/>\nThe surface area of a cube = 6 (Side)\u00b2<br \/>\nThe volume of a cube = (Side)\u00b3<br \/>\nLet the length of the side of the cube = \\(\\sqrt{2}\\)<br \/>\nThe surface area of a cube = 6 (\u221a2)\u00b2<br \/>\n= 6 (2)<br \/>\n= 12<br \/>\nThe volume of a cube = (\u221a2)\u00b3<br \/>\nThe surface area of a cube will always be rational irrespective the number is rational or irrational<br \/>\nThere is no possible value of s<\/p>\n<p>Question 103.<br \/>\n<strong>REASONING<\/strong><br \/>\nLet a and b be positive numbers. Explain why \\(\\sqrt{ab}\\) lies between a and b on a number line. (Hint: Let a&lt; b and multiply each side of a &lt; b by a. Then let a &lt; b and multiply each side by b.)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41989\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-103.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 103\" width=\"584\" height=\"193\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-103.png 584w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-103-300x99.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 104.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says that you can rationalize the denominator of the expression \\(\\frac{2}{4+\\sqrt[3]{5}}\\) by multiplying the numerator and denominator by 4 &#8211; \\(\\sqrt[3]{5}\\). Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\nYou can rationalize the denominator of the expression \\(\\frac{2}{4+\\sqrt[3]{5}}\\) by multiplying the numerator and denominator by 4 &#8211; \\(\\sqrt[3]{5}\\).<br \/>\nWe will rationalize a radical to make that radical a rational number<br \/>\nA &#8220;Rational number&#8221; is a number that can be written in the form of \\(\\frac{p}{q}\\)<br \/>\nWe will see whether we can rationalize the denominator or not in the given fraction<br \/>\n(4 &#8211; \\(\\sqrt[3]{5}\\)) \u00d7 (4 + \\(\\sqrt[3]{5}\\))<br \/>\n= 4\u00b2 &#8211; (\\(\\sqrt[3]{5}\\) \u00d7 \\(\\sqrt[3]{5}\\))<br \/>\n= 16 &#8211; (\\(\\sqrt[3]{5}\\) \u00d7 \\(\\sqrt[3]{5}\\))<br \/>\nFrom the above value,<br \/>\nWe can observe that the denominator can&#8217;t be rationalized<br \/>\nWe can conclude that your friend is not correct<\/p>\n<p>Question 105.<br \/>\n<strong>PROBLEM -SOLVING<\/strong><br \/>\nThe ratio of consecutive terms \\(\\frac{a_{n}}{a_{n}-1}\\) in the Fibonacci sequence gets closer and closer to the golden ratio \\(\\frac{1+\\sqrt{5}}{2}\\) as n increases. Find the term that precedes 610 in the sequence.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41990\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-105.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 105.1\" width=\"265\" height=\"528\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-105.1.png 265w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-105.1-151x300.png 151w\" sizes=\"(max-width: 265px) 100vw, 265px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41991\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-105.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 105.2\" width=\"335\" height=\"141\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-105.2.png 335w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-105.2-300x126.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><\/p>\n<p>Question 106.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nUse the golden ratio \\(\\frac{1+\\sqrt{5}}{2}\\) and the golden ratio conjugate \\(\\frac{1-\\sqrt{5}}{2}\\) for each of the following.<br \/>\na. Show that the golden ratio and golden ratio conjugate are both solutions of x<sup>2<\/sup> &#8211; x &#8211; 1 = 0.<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; x &#8211; 1 = 0<br \/>\nSolution1, Solution 2 = \\(\\frac{-b + \\sqrt{b\u00b2 &#8211; 4 a c}}{2 a}\\), \\(\\frac{-b &#8211; \\sqrt{b\u00b2 &#8211; 4 a c}}{2 a}\\)<br \/>\nCompare the give equation with<br \/>\nax\u00b2 +\u00a0 x + c = 0<br \/>\na = 1, b = -1, and c = -1<br \/>\nSolution1, Solution 2 = \\(\\frac{1 + \\sqrt{(-1)\u00b2 &#8211; 4 (1) (-1)}}{2 (1)}\\), \\(\\frac{1 &#8211; \\sqrt{(-1)\u00b2 &#8211; 4 (1) (-1)}}{2 (1)}\\)<br \/>\nSolution1, Solution 2 = \\(\\frac{1 + \\sqrt{1 + 4}}{2}\\), \\(\\frac{1 &#8211; \\sqrt{1 + 4}}{2}\\)<br \/>\nSolution1, Solution 2 = \\(\\frac{1 + \\sqrt{5}}{2}\\), \\(\\frac{1 &#8211; \\sqrt{5}}{2}\\)<br \/>\nThe golden ratio and golden ratio conjugate are both solutions of the given equation<\/p>\n<p>b. Construct a geometric diagram that has the golden ratio as the length of a part of the diagram.<br \/>\nAnswer:<br \/>\nThe golden ratio is: \\(\\frac{1 + \\sqrt{5}}{2}\\)<br \/>\n\\(\\frac{1 + \\sqrt{5}}{2}\\) = 1.61<br \/>\nThe representation of the golden ratio as the length of the part of the diagram is:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-108786\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-4.png\" alt=\"\" width=\"429\" height=\"142\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-4.png 429w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-4-300x99.png 300w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><\/p>\n<p>Question 107.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nUse the special product pattern (a + b)(a<sup>2<\/sup> &#8211; ab + b<sup>2<\/sup>) = a<sup>3<\/sup> + b<sup>3<\/sup> to simplify the expression \\(\\frac{2}{\\sqrt[3]{x}+1}\\). Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41992\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-107.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 107\" width=\"542\" height=\"357\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-107.png 542w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-107-300x198.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p>Graph the linear equation. Identify the x-intercept.<br \/>\nQuestion 108.<br \/>\ny = x &#8211; 4<br \/>\nAnswer:<br \/>\ny = x &#8211; 4<br \/>\ny = mx + c<br \/>\nm is the slope<br \/>\nc is the y-intercept<br \/>\nTo find the x-intercept,put y = 0<br \/>\nx &#8211; 4 = 0<br \/>\nx = 4<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-108894\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-5.png\" alt=\"\" width=\"483\" height=\"495\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-5.png 483w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-5-293x300.png 293w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><br \/>\nThe x-intercept of the linear equation is: 4<\/p>\n<p>Question 109.<br \/>\ny = -2x + 6<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41993\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-109.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 109\" width=\"586\" height=\"350\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-109.png 586w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-109-300x179.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 110.<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x &#8211; 1<br \/>\nAnswer:<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x &#8211; 1<br \/>\ny = mx + c<br \/>\nWhere,<br \/>\nm is the slope<br \/>\nc is the y-intercept<br \/>\nTo find the x-intercept,put y = 0<br \/>\nSo,<br \/>\n&#8211;\\(\\frac{1}{3}\\)x &#8211; 1 = 0<br \/>\n&#8211;\\(\\frac{1}{3}\\)x = 1<br \/>\nx = -3<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-108898\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-6.png\" alt=\"\" width=\"490\" height=\"531\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-6.png 490w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-6-277x300.png 277w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nThe x-intercept of the linear equation is: -3<\/p>\n<p>Question 111.<br \/>\ny = \\(\\frac{3}{2}\\)x + 6<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41994\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-111.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 111\" width=\"571\" height=\"345\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-111.png 571w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-111-300x181.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><br \/>\nQuestion 112.<br \/>\n32 = 2<sup>x<\/sup><br \/>\nAnswer:<br \/>\n32 = 2^x<br \/>\n2^5 = 2^x<br \/>\nx = 5<\/p>\n<p>Question 113.<br \/>\n27<sup>x<\/sup> = 3<sup>x &#8211; 6<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41995\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-113.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 113\" width=\"487\" height=\"327\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-113.png 487w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-113-300x201.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><\/p>\n<p>Question 114.<br \/>\n(\\(\\frac{1}{6}\\))<sup>2x<\/sup> = 216<sup>1 &#8211; x<\/sup><br \/>\nAnswer:<br \/>\n(\\(\\frac{1}{6}\\))<sup>2x<\/sup> = 216<sup>1 &#8211; x<\/sup><br \/>\n\\(\\frac{1}{x}\\) = x^-1<br \/>\n[6^-1]^2 x = [6^3]^1 &#8211; x<br \/>\n6^[-2x] = 6^[3(1 &#8211; x)]<br \/>\n-2x = 3 (1 &#8211; x)<br \/>\n-2x = 3 &#8211; 3x<br \/>\n-2x + 3x = 3<br \/>\nx = 3<\/p>\n<p>Question 115.<br \/>\n625<sup>x<\/sup> = (\\(\\frac{1}{25}\\))<sup>x + 2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41996\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-115.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 115\" width=\"557\" height=\"533\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-115.png 557w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-115-300x287.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<h3><a id=\"Lesson_9.2_Solving_Quadratic_Equations_by_Graphing\"><\/a>Lesson 9.2 Solving Quadratic Equations by Graphing<\/h3>\n<p><strong>Essential Question<\/strong> How can you use a graph to solve a quadratic equation in one variable?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35284\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 1\" width=\"279\" height=\"245\" \/><br \/>\nBased on what you learned about the x-intercepts of a graph in Section 3.4, it follows that the x-intercept of the graph of the linear equation<br \/>\ny = ax + b &#8212;-&gt; 2 variables<br \/>\nis the same value as the solution of<br \/>\nax + b = 0 &#8212;&#8211;&gt; 1 variable<br \/>\nYou can use similar reasoning to solve quadratic equations.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Solving a Quadratic Equation by Graphing<br \/>\nWork with a partner.<br \/>\na. Sketch the graph of y = x<sup>2<\/sup> &#8211; 2x.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35285\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 2\" width=\"247\" height=\"250\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-108960\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-7.png\" alt=\"\" width=\"478\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-7.png 478w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-7-285x300.png 285w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><br \/>\nb. What is the definition of an x-intercept of a graph? How many x-intercepts does this graph have? What are they?<br \/>\nAnswer:<br \/>\nThe\u00a0x-intercept\u00a0is the point where a line crosses the\u00a0x-axis,<br \/>\nThere are 2 points where a line crosses the x-axis<br \/>\nThe 2 points that a line crosses the x-axis are 0, 2<\/p>\n<p>c. What is the definition of a solution of an equation in x? How many solutions does the equation x<sup>2<\/sup> &#8211; 2x = 0 have? What are they?<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 2x = 0<br \/>\nx (x &#8211; 2) = 0<br \/>\nx = 0 or x &#8211; 2 = 0<br \/>\nx = 0 or x = 0 + 2<br \/>\nx = 0 or x = 2<br \/>\nThe 2 solutions of the given equation are 0 and 2<\/p>\n<p>d. Explain how you can verify the solutions you found in part (c).<br \/>\nAnswer:<br \/>\nPut x = 0 in the given equation<br \/>\n0 &#8211; 2 (0) = 0<br \/>\n0 = 0<br \/>\nPut x = 2 in the given equation<br \/>\n2\u00b2 &#8211; 2 (2) = 0<br \/>\n4 &#8211; 4 = 0<br \/>\n0 = 0<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Solving Quadratic Equations by Graphing<br \/>\nWork with a partner. Solve each equation by graphing.<br \/>\na. x<sup>2<\/sup> &#8211; 4 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109018\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-8.png\" alt=\"\" width=\"487\" height=\"501\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-8.png 487w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-8-292x300.png 292w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><br \/>\nThe solutions that satisfy the above equation i.e., x-intercepts are -2 and 2<br \/>\nb. x<sup>2<\/sup> + 3x = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109577\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-9.png\" alt=\"\" width=\"485\" height=\"494\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-9.png 485w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-9-295x300.png 295w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nThe solutions that satisfy the above equation i.e., x-intercepts are: 0 and -3<\/p>\n<p>c. -x<sup>2<\/sup> + 2x = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109586\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-14.png\" alt=\"\" width=\"479\" height=\"501\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-14.png 479w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-14-287x300.png 287w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nThe solutions that satisfy the above equation i.e., x-intercepts are 0 and -2<\/p>\n<p>d. x<sup>2<\/sup> &#8211; 2x + 1 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109579\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-11.png\" alt=\"\" width=\"470\" height=\"509\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-11.png 470w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-11-277x300.png 277w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><br \/>\nThe solution that satisfies the above equation i.e., x-intercepts is: 1<\/p>\n<p>e. x<sup>2<\/sup> &#8211; 3x + 5 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109580\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-12.png\" alt=\"\" width=\"472\" height=\"495\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-12.png 472w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-12-286x300.png 286w\" sizes=\"(max-width: 472px) 100vw, 472px\" \/><br \/>\nThe approximate solutions that satisfy the above equation i.e., x-intercepts are 0.9 and 2.1<\/p>\n<p>f. -x<sup>2<\/sup> + 3x &#8211; 6 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109581\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-13.png\" alt=\"\" width=\"482\" height=\"492\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-13.png 482w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-13-294x300.png 294w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><br \/>\nThe solutions that satisfy the above equation i.e., x-intercepts are 1 and 2<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you use a graph to solve a quadratic equation in one variable?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35286\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 3\" width=\"225\" height=\"182\" \/><br \/>\nAnswer:<br \/>\ny = ax + b &#8212;-&gt; 2 variables<br \/>\nis the same value as the solution of<br \/>\nax + b = 0 &#8212;&#8211;&gt; 1 variable<br \/>\nYou can use similar reasoning to solve quadratic equations.<\/p>\n<p>Question 4.<br \/>\nAfter you find a solution graphically, how can you check your result algebraically? Check your solutions for parts (a)-(d) in Exploration 2 algebraically.<br \/>\nAnswer:<br \/>\na. x\u00b2 &#8211; 4 = 0<br \/>\nThe solutions of the given equation are -2 and 2<br \/>\n(-2)\u00b2 -4 = 0<br \/>\n4 &#8211; 4 = 0<br \/>\n2\u00b2 &#8211; 4 = 0<br \/>\n4 &#8211; 4 = 0<br \/>\n0 = 0<br \/>\nb. x\u00b2 + 3x = 0<br \/>\nThe solutions of the given equation are 0 and -3<br \/>\n0\u00b2 + 3 (0) = 0<br \/>\n0 + 0 = 0<br \/>\n0 = 0<br \/>\n(-3)\u00b2 + 3 (-3) = 0<br \/>\n9 &#8211; 9 = 0<br \/>\n0 = 0<br \/>\nc. -x\u00b2 + 2x = 0<br \/>\nThe solutions of the given equation are 0 and 2<br \/>\n0\u00b2 + 2 (0) = 0<br \/>\n0 + 0 = 0<br \/>\n0 = 0<br \/>\n-(2)\u00b2 + 2 (2) = 0<br \/>\n4 &#8211; 4 = 0<br \/>\n0 = 0<br \/>\nd. x\u00b2 &#8211; 2x + 1 = 0<br \/>\nThe solution of the given equation are 1<br \/>\n1\u00b2 &#8211; 2 (1) + 1 = 0<br \/>\n1 &#8211; 2 + 1 = 0<br \/>\n2 &#8211; 2 = 0<br \/>\n0 = 0<\/p>\n<p>Question 5.<br \/>\nHow can you determine graphically that a quadratic equation has no solution?<br \/>\nAnswer:<br \/>\nFor any quadratic equation, the graph will be a parabola. If the parabola does not cross or intersect the x-axis, then the equation has no real solution. And no real solution does not mean that there is no solution, but that the solutions are not real numbers.<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the equation by graphing. Check your solutions.<\/strong><br \/>\nQuestion 1.<br \/>\nx<sup>2<\/sup> &#8211; x &#8211; 2 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109587\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-15.png\" alt=\"\" width=\"568\" height=\"516\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-15.png 568w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-15-300x273.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><br \/>\nWe can observe the solutions that satisfy the given equation i.e., x-intercepts from the graph are -1 and 2<br \/>\n(-1)\u00b2 &#8211; (-1) &#8211; 2 = 0<br \/>\n1 +1 &#8211; 2 = 0<br \/>\n2 &#8211; 2 = 0<br \/>\n0 = 0<br \/>\n(2)\u00b2 &#8211; 2 + 2 = 0<br \/>\n4 &#8211; 2 + 2 = 0<br \/>\n2 &#8211; 2 = 0<br \/>\n0 = 0<\/p>\n<p>Question 2.<br \/>\nx<sup>2<\/sup> + 7x = -10<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109588\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-16.png\" alt=\"\" width=\"473\" height=\"500\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-16.png 473w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-16-284x300.png 284w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><br \/>\nWe can observe the solutions that satisfy the given equation i.e., x-intercepts from the graph are: -2 and -5<br \/>\n(-2)\u00b2 + 7(-2) + 10 = 0<br \/>\n4 &#8211; 14 + 10 = 0<br \/>\n14 &#8211; 14 = 0<br \/>\n0 = 0<br \/>\n(-5)\u00b2 + 7(-5) + 10 = 0<br \/>\n25 &#8211; 35 + 10 = 0<br \/>\n35 &#8211; 35 = 0<br \/>\n0 = 0<\/p>\n<p>Question 3.<br \/>\nx<sup>2<\/sup> + x = 12<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109589\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-17.png\" alt=\"\" width=\"474\" height=\"498\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-17.png 474w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-17-286x300.png 286w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><br \/>\nWe can observe the solutions that satisfy the given equation i.e., x-intercepts from the graph are -4 and 3<br \/>\n(-4)\u00b2 -4 &#8211; 12 = 0<br \/>\n16 &#8211; 4 &#8211; 12 = 0<br \/>\n12 &#8211; 12 = 0<br \/>\n0 = 0<br \/>\n(3)\u00b2 + 3 &#8211; 12 = 0<br \/>\n9 &#8211; 12 + 3 = 0<br \/>\n12 &#8211; 12 = 0<br \/>\n0 = 0<\/p>\n<p><strong>Solve the equation by graphing.<\/strong><br \/>\nQuestion 4.<br \/>\nx<sup>2<\/sup> + 36 = 12x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109592\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-18.png\" alt=\"\" width=\"475\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-18.png 475w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-18-283x300.png 283w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><br \/>\nThe solution of the given equation is 6<\/p>\n<p>Question 5.<br \/>\nx<sup>2<\/sup> + 4x = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109594\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-19.png\" alt=\"\" width=\"475\" height=\"500\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-19.png 475w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-19-285x300.png 285w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><br \/>\nThe solutions of the given equation are 0 and -4<\/p>\n<p>Question 6.<br \/>\nx<sup>2<\/sup> + 10x = -25<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109595\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-20.png\" alt=\"\" width=\"479\" height=\"496\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-20.png 479w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-20-290x300.png 290w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nThe solution of the given equation is -5<\/p>\n<p>Question 7.<br \/>\nx<sup>2<\/sup> = 3x &#8211; 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109614\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-21.png\" alt=\"\" width=\"479\" height=\"501\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-21.png 479w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-21-287x300.png 287w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nThere are no real solutions for the given equation<\/p>\n<p>Question 8.<br \/>\nx<sup>2<\/sup> + 7x = -6<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109617\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-22.png\" alt=\"\" width=\"484\" height=\"499\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-22.png 484w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-22-291x300.png 291w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><br \/>\nThe solutions of the given equation are -1 and -6<\/p>\n<p>Question 9.<br \/>\n2x + 5 = -x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109618\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-23.png\" alt=\"\" width=\"476\" height=\"498\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-23.png 476w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-23-287x300.png 287w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><br \/>\nThere are no real solutions for the given equation<\/p>\n<p>Question 10.<br \/>\nGraph f(x) = x<sup>2<\/sup> + x &#8211; 6. Find the zeros of f.<br \/>\nAnswer:<br \/>\nf(x) = x\u00b2 + x &#8211; 6<br \/>\nTo find the zeroes of f(x), make f(x) = 0<br \/>\nx\u00b2 + x &#8211; 6 = 0<br \/>\nx\u00b2 + 3x &#8211; 2x &#8211; 6 = 0<br \/>\nx (x + 3) -2 (x + 3) = 0<br \/>\n(x &#8211; 2) (x + 3) = 0<br \/>\nx &#8211; 2 = 0 or x + 3 = 0<br \/>\nx = 2 or x = -3<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109623\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-24.png\" alt=\"\" width=\"480\" height=\"498\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-24.png 480w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-24-289x300.png 289w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><br \/>\nThe zeroes of the given equation are -3 and 2<\/p>\n<p>Question 11.<br \/>\nGraph f(x) = -x<sup>2<\/sup> + 2x + 2. Approximate the zeros of f to the nearest tenth.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-194285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.2_11-243x300.png\" alt=\"Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.2_11\" width=\"243\" height=\"300\" \/><\/p>\n<p>Question 12.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nAfter how many seconds is the football 65 feet above the ground?<br \/>\nAnswer:<br \/>\nThe function &#8216;h&#8217; that represents the height (h) in feet of the football after t seconds is:<br \/>\nh = -16t\u00b2 + 75t + 2<br \/>\n-16t\u00b2 + 75t + 2 = 65<br \/>\n-16t\u00b2 + 75t + 2 &#8211; 65 = 0<br \/>\n-16t\u00b2 + 75t &#8211; 63 = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109640\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-26.png\" alt=\"\" width=\"470\" height=\"471\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-26.png 470w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-26-300x300.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-26-150x150.png 150w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><br \/>\nThe football is 65 feet above the ground after 1 second and after about 3.8 seconds<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_by_Graphing_9.2_Exercises\"><\/a>Solving Quadratic Equations by Graphing 9.2 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat is a quadratic equation?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41997\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 1\" width=\"591\" height=\"53\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-1.png 591w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-1-300x27.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich equation does not belong with the other three? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35287\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-4.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 4\" width=\"501\" height=\"43\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-4.png 501w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-4-300x26.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109794\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-28.png\" alt=\"\" width=\"758\" height=\"514\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-28.png 758w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-28-300x203.png 300w\" sizes=\"(max-width: 758px) 100vw, 758px\" \/><br \/>\nx\u00b2 &#8211; 7x + 12 = 0 does not belong with the other three<\/p>\n<p>Question 3.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow can you use a graph to find the number of solutions of a quadratic equation?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41998\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 3\" width=\"575\" height=\"83\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-3.png 575w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-3-300x43.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow are solutions, roots, x-intercepts, and zeros related?<br \/>\nAnswer:<br \/>\nZeroes, roots, and x-intercepts are all names for values that make a function equal to zero. Zeros, roots, or x-intercepts of a function f(x) are the values of x where the graph of the function f crosses the x-axis.<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u20138, use the graph to solve the equation.<\/strong><br \/>\nQuestion 5.<br \/>\n-x<sup>2<\/sup> + 2x + 3 = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35288\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 5\" width=\"155\" height=\"150\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-41999\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 5\" width=\"538\" height=\"58\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-5.png 538w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-5-300x32.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 6.<br \/>\nx<sup>2<\/sup> &#8211; 6x + 8 = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35289\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-6.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 6\" width=\"150\" height=\"145\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35289\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-6.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 6\" width=\"150\" height=\"145\" \/><br \/>\nWe can observe that there are two x-intercepts i.e., two solutions for the\u00a0 given equation<br \/>\nThe two x-intercepts of the given equation are: 2 and 4<\/p>\n<p>Question 7.<br \/>\nx<sup>2<\/sup> + 8x + 16 = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35290\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 7\" width=\"165\" height=\"153\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42000\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 7\" width=\"575\" height=\"56\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-7.png 575w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-7-300x29.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 8.<br \/>\n-x<sup>2<\/sup> &#8211; 4x &#8211; 6 = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35291\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-8.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 8\" width=\"143\" height=\"150\" \/><br \/>\nAnswer:<br \/>\nThere are no x-intercepts i.e., no real solutions for the\u00a0 given equation<\/p>\n<p><strong>In Exercises 9\u201312, write the equation in standard form.<\/strong><br \/>\nQuestion 9.<br \/>\n4x<sup>2<\/sup> = 12<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42001\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 9\" width=\"545\" height=\"139\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-9.png 545w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-9-300x77.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 10.<br \/>\n-x<sup>2<\/sup> = 15<br \/>\nAnswer:<br \/>\n-x\u00b2 = 15<br \/>\n-x\u00b2 &#8211; 15 = 0<br \/>\n&#8211; (x\u00b2 + 15) = 0<br \/>\nx\u00b2 + 15 = 0<\/p>\n<p>Question 11.<br \/>\n2x &#8211; x<sup>2<\/sup> = 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42002\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 11\" width=\"440\" height=\"162\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-11.png 440w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-11-300x110.png 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><\/p>\n<p>Question 12.<br \/>\n5 + x = 3x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n5 + x = 3x\u00b2<br \/>\n5 + x &#8211; 3x\u00b2 = 0<br \/>\n&#8211; (3x\u00b2 &#8211; x &#8211; 5) = 0<br \/>\n5 + x &#8211; 3x\u00b2 = 0<\/p>\n<p><strong>In Exercises 13\u201324, solve the equation by graphing.<\/strong><br \/>\nQuestion 13.<br \/>\nx<sup>2<\/sup> &#8211; 5x = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42003\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 13\" width=\"557\" height=\"339\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-13.png 557w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-13-300x183.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 14.<br \/>\nx<sup>2<\/sup> &#8211; 4x + 4 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109814\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-29.png\" alt=\"\" width=\"479\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-29.png 479w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-29-285x300.png 285w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nThe solution of the given equation is 2<\/p>\n<p>Question 15.<br \/>\nx<sup>2<\/sup> &#8211; 2x + 5 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42004\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 15\" width=\"535\" height=\"336\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-15.png 535w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-15-300x188.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Question 16.<br \/>\nx<sup>2<\/sup> &#8211; 6x &#8211; 7 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109815\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-30.png\" alt=\"\" width=\"486\" height=\"505\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-30.png 486w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-30-289x300.png 289w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><br \/>\nThe solutions of the given equation are -1 and 7<\/p>\n<p>Question 17.<br \/>\nx<sup>2<\/sup> &#8211; 6x = 9<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42005\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 17\" width=\"538\" height=\"455\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-17.png 538w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-17-300x254.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 18.<br \/>\n-x<sup>2<\/sup> = 8x + 20<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109817\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-31.png\" alt=\"\" width=\"476\" height=\"497\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-31.png 476w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-31-287x300.png 287w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><br \/>\nThere are no real solutions for the given equation<\/p>\n<p>Question 19.<br \/>\nx<sup>2<\/sup> = -1 &#8211; 2x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42006\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 19\" width=\"572\" height=\"445\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-19.png 572w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-19-300x233.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 20.<br \/>\nx<sup>2<\/sup> = -x &#8211; 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109818\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-32.png\" alt=\"\" width=\"480\" height=\"494\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-32.png 480w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-32-291x300.png 291w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><br \/>\nThere are no real solutions for the given equation<\/p>\n<p>Question 21.<br \/>\n4x &#8211; 12 = -x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42007\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 21\" width=\"553\" height=\"444\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-21.png 553w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-21-300x241.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 22.<br \/>\n5x &#8211; 6 = x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109819\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-33.png\" alt=\"\" width=\"481\" height=\"503\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-33.png 481w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-33-287x300.png 287w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\nThe solutions of the given equation are 2 and 3<\/p>\n<p>Question 23.<br \/>\nx<sup>2<\/sup> &#8211; 2 = -x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42008\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 23\" width=\"559\" height=\"439\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-23.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-23-300x236.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 24.<br \/>\n16 + x<sup>2<\/sup> = -8x<br \/>\nAnswer:<br \/>\n16 + x\u00b2 = -8x<br \/>\nx\u00b2 + 8x + 16 = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109822\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-34.png\" alt=\"\" width=\"473\" height=\"498\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-34.png 473w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-34-285x300.png 285w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><br \/>\nThe solution of the given equation is -4<\/p>\n<p>Question 25.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving x<sup>2<\/sup> + 3x = 18 by graphing.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35292\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 9\" width=\"329\" height=\"233\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-9.png 329w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-9-300x212.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42009\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 25\" width=\"512\" height=\"483\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-25.png 512w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-25-300x283.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving x<sup>2<\/sup> + 6x + 9 = 0 by graphing.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35293\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-10.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 10\" width=\"314\" height=\"227\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-10.png 314w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-10-300x217.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-109827\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-35.png\" alt=\"\" width=\"476\" height=\"501\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-35.png 476w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-35-285x300.png 285w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><br \/>\nThe solution of the given equation is x = -3<\/p>\n<p>Question 27.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe height y (in yards) of a flop shot in golf can be modeled by y = -x<sup>2<\/sup> + 5x, where x is the horizontal distance (in yards).<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35294\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 11\" width=\"176\" height=\"115\" \/><br \/>\na. Interpret the x-intercepts of the graph of the equation.<br \/>\nb. How far away does the golf ball land?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42010\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 27\" width=\"548\" height=\"473\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-27.png 548w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-27-300x259.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe height h (in feet) of an underhand volleyball serve can be modeled by h = -16t<sup>2<\/sup> + 30t + 4, where t is the time (in seconds).<br \/>\na. Do both t-intercepts of the graph of the function have meaning in this situation? Explain.<br \/>\nAnswer:<br \/>\nh = -16t\u00b2 + 30t + 4<br \/>\nWhere,<br \/>\nt is the time in seconds<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-110079\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-36.png\" alt=\"\" width=\"481\" height=\"499\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-36.png 481w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-36-289x300.png 289w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\nThe two t-intercepts of the given equation are 0 and 2<br \/>\nFrom the two intercepts of t,<br \/>\nWe can observe that both intercepts have the meaning<br \/>\nWhen t = 0,<br \/>\nThe underhand volleyball can&#8217;t be served<br \/>\nWhen t = 2,<br \/>\nThe underhand vollyball can be served<br \/>\nThe two intercepts of t have the meaning in this situation<\/p>\n<p>b. No one receives the serve. After how many seconds does the volleyball hit the ground?<br \/>\nAnswer:<br \/>\nWe can observe that the t-intercepts are 0 and 2<br \/>\nThe time that the volleyball hit the ground = 2 &#8211; 0 = 2 seconds<br \/>\nAfter 2 seconds, the volleyball hit the ground<\/p>\n<p><strong>In Exercises 29\u201336, solve the equation by using Method 2 from Example 3.<\/strong><br \/>\nQuestion 29.<br \/>\nx<sup>2<\/sup> = 10 &#8211; 3x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42011\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 29\" width=\"581\" height=\"443\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-29.png 581w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-29-300x229.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 30.<br \/>\n2x &#8211; 3 = x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n2x &#8211; 3 = x\u00b2<br \/>\ny = x\u00b2<br \/>\ny = 2x &#8211; 3<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-110292\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-37.png\" alt=\"\" width=\"476\" height=\"499\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-37.png 476w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-37-286x300.png 286w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><br \/>\nThe given equation does not have any real solution<\/p>\n<p>Question 31.<br \/>\n5x &#8211; 7 = x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42012\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 31\" width=\"580\" height=\"412\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-31.png 580w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-31-300x213.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 32.<br \/>\nx<sup>2<\/sup> = 6x &#8211; 5<br \/>\nAnswer:<br \/>\nx\u00b2 = 6x &#8211; 5<br \/>\ny = x\u00b2<br \/>\ny = 6x &#8211; 5<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-110296\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-38.png\" alt=\"\" width=\"470\" height=\"495\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-38.png 470w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-38-285x300.png 285w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><br \/>\nThe graphs of two equations intersect at (1, 1)<br \/>\nThe solution of the given equation is 1<\/p>\n<p>Question 33.<br \/>\nx<sup>2<\/sup> + 12x = -20<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42013\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 33\" width=\"552\" height=\"425\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-33.png 552w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-33-300x231.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 34.<br \/>\nx<sup>2<\/sup> + 8x = 9<br \/>\nAnswer:<br \/>\nx\u00b2\u00a0 + 8x = 9<br \/>\nx\u00b2 = -8x + 9<br \/>\ny = x\u00b2<br \/>\ny = -8x + 9<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-110300\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-39.png\" alt=\"\" width=\"475\" height=\"495\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-39.png 475w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-39-288x300.png 288w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><br \/>\nThe graphs of two equations intersect at (1, 1)<br \/>\nThe solution of the given equation is 1<\/p>\n<p>Question 35.<br \/>\n-x<sup>2<\/sup> &#8211; 5 = -2x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42014\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 35\" width=\"453\" height=\"408\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-35.png 453w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-35-300x270.png 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/p>\n<p>Question 36.<br \/>\n-x<sup>2<\/sup> &#8211; 4 = -4x<br \/>\nAnswer:<br \/>\n&#8211; x\u00b2 &#8211; 4 = -4x<br \/>\n-x\u00b2 = -4x + 4<br \/>\nx\u00b2 = 4x &#8211; 4<br \/>\ny = x\u00b2<br \/>\ny = 4x &#8211; 4<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-110303\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-40.png\" alt=\"\" width=\"476\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-40.png 476w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-40-283x300.png 283w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><br \/>\nThe graphs of two equations intersect at (2, -4)<br \/>\nThe solution of the given equation is 2<\/p>\n<p><strong>In Exercises 37\u201342, find the zero(s) of f.<\/strong><br \/>\nQuestion 37.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35295\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-12.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 12\" width=\"148\" height=\"152\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42015\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 37\" width=\"387\" height=\"589\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-37.png 387w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-37-197x300.png 197w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><\/p>\n<p>Question 38.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35296\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 13\" width=\"185\" height=\"155\" \/><br \/>\nAnswer:<br \/>\nf(x) = (x + 1) (x\u00b2 + 6x + 8)<br \/>\nf(x) = 0<br \/>\n(x + 1) (x\u00b2 + 6x + 8) = 0<br \/>\nx + 1 = 0 (or)\u00a0 x\u00b2 + 6x + 8 = 0<br \/>\nx + 1 = 0 (or)\u00a0 x\u00b2 + 4x + 2x + 8 = 0<br \/>\nx + 1 = 0 (or)\u00a0 x (x + 4) + 2 (x + 4) = 0<br \/>\nx + 1 = 0 (or) (x + 2) (x + 4) = 0<br \/>\nx + 1 = 0 (or) x + 2 = 0 (or) x + 4 = 0<br \/>\nx = -1 (or) x = -2 (or) x = -4<br \/>\nThe zeroes of the given function are -1, -2, and -4<\/p>\n<p>Question 39.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35297\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-14.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 14\" width=\"196\" height=\"150\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42016\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 39\" width=\"452\" height=\"482\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-39.png 452w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-39-281x300.png 281w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><\/p>\n<p>Question 40.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35298\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 15\" width=\"193\" height=\"154\" \/><br \/>\nAnswer:<br \/>\nf(x) = (x &#8211; 5) (-x\u00b2 + 3x &#8211; 3)<br \/>\nf(x) = 0<br \/>\n(x &#8211; 5) (-x\u00b2 + 3x &#8211; 3) = 0<br \/>\nx &#8211; 5 = 0 (or)\u00a0 -x\u00b2 + 3x &#8211; 3 = 0<br \/>\n-x\u00b2 + 3x &#8211; 3 = 0,<br \/>\nx &#8211; 5 = 0<br \/>\nx = 5<br \/>\nThe zero of the given function is -5<\/p>\n<p>Question 41.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35299\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-16.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 16\" width=\"190\" height=\"158\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42017\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-41.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 41.1\" width=\"465\" height=\"445\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-41.1.png 465w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-41.1-300x287.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42018\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-41.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 41.2\" width=\"475\" height=\"454\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-41.2.png 475w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-41.2-300x287.png 300w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><\/p>\n<p>Question 42<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35300\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 17\" width=\"188\" height=\"169\" \/><br \/>\nAnswer:<br \/>\nf(x) = (x\u00b2 + 1) (x\u00b2 &#8211; x &#8211; 2)<br \/>\nf(x) = 0<br \/>\n(x\u00b2 + 1) (x\u00b2 &#8211; x &#8211; 2) = 0<br \/>\nx\u00b2 + 1 = 0 (or)\u00a0 x\u00b2 &#8211; x &#8211; 2 = 0<br \/>\nx\u00b2 + 1 = 0 (or)\u00a0 x\u00b2 + x &#8211; 2x &#8211; 2 = 0<br \/>\nx\u00b2 + 1 = 0 (or)\u00a0 x (x + 1) &#8211; 2 (x + 1) = 0<br \/>\nx\u00b2 + 1 = 0 (or) (x + 1) (x &#8211; 2) = 0<br \/>\nx\u00b2 + 1 = 0 (or) x + 1 = 0 (or) x &#8211; 2 = 0<br \/>\nx\u00b2 = -1 (or) x = -1 (or) x = 2<br \/>\nx\u00b2 + 1 = 0,<br \/>\nThe zeroes of the given function are -1, and 2<\/p>\n<p><strong>In Exercises 43\u201346, approximate the zeros of f to the nearest tenth.<\/strong><br \/>\nQuestion 43.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35301\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-18.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 18\" width=\"146\" height=\"156\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42019\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 43\" width=\"572\" height=\"591\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-43.png 572w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-43-290x300.png 290w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 44.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35302\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 19\" width=\"148\" height=\"165\" \/><br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35303\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-20.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 20\" width=\"149\" height=\"159\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42020\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 45\" width=\"549\" height=\"598\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-45.png 549w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-45-275x300.png 275w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 46.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35304\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 21\" width=\"156\" height=\"156\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-21.png 156w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-21-150x150.png 150w\" sizes=\"(max-width: 156px) 100vw, 156px\" \/><br \/>\nAnswer:<br \/>\nThere are two x intercepts, one between 0 and 1, and the other between 5 and 6.<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"73\">X<\/td>\n<td width=\"73\">0.1<\/td>\n<td width=\"73\">0.2<\/td>\n<td width=\"73\">0.3<\/td>\n<td width=\"73\">0.4<\/td>\n<td width=\"73\">0.5<\/td>\n<td width=\"73\">0.6<\/td>\n<td width=\"73\">0.7<\/td>\n<td width=\"73\">0.8<\/td>\n<td width=\"73\">0.9<\/td>\n<\/tr>\n<tr>\n<td width=\"73\">F(x)<\/td>\n<td width=\"73\">-1.41<\/td>\n<td width=\"73\">-0.24<\/td>\n<td width=\"73\">-0.29<\/td>\n<td width=\"73\">0.24<\/td>\n<td width=\"73\">0.75<\/td>\n<td width=\"73\">1.24<\/td>\n<td width=\"73\">1.71<\/td>\n<td width=\"73\">2.16<\/td>\n<td width=\"73\">2.59<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Tabulating x values between 5 and 6<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"73\">X<\/td>\n<td width=\"73\">5.1<\/td>\n<td width=\"73\">5.2<\/td>\n<td width=\"73\">5.3<\/td>\n<td width=\"73\">5.4<\/td>\n<td width=\"73\">5.5<\/td>\n<td width=\"73\">5.6<\/td>\n<td width=\"73\">5.7<\/td>\n<td width=\"73\">5.8<\/td>\n<td width=\"73\">5.9<\/td>\n<\/tr>\n<tr>\n<td width=\"73\">F(x)<\/td>\n<td width=\"73\">2.59<\/td>\n<td width=\"73\">2.16<\/td>\n<td width=\"73\">1.71<\/td>\n<td width=\"73\">1.24<\/td>\n<td width=\"73\">0.75<\/td>\n<td width=\"73\">0.24<\/td>\n<td width=\"73\">-0.29<\/td>\n<td width=\"73\">-0.84<\/td>\n<td width=\"73\">-1.41<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Thus the function has zeros at x = 0.4, 0.5 approximate to the nearest tenth.<\/p>\n<p><strong>In Exercises 47\u201352, graph the function. Approximate the zeros of the function to the nearest tenth, if necessary.<\/strong><br \/>\nQuestion 47.<br \/>\nf(x) = x<sup>2<\/sup> + 6x + 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42021\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-47.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 47.1\" width=\"480\" height=\"470\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-47.1.png 480w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-47.1-300x294.png 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42022\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-47.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 47.2\" width=\"581\" height=\"438\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-47.2.png 581w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-47.2-300x226.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 48.<br \/>\nf(x) = x<sup>2<\/sup> &#8211; 3x + 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-194286\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.2_48-259x300.png\" alt=\"Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.2_48\" width=\"259\" height=\"300\" \/><\/p>\n<p>Question 49.<br \/>\ny = -x<sup>2<\/sup> + 4x &#8211; 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42023\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-49.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 49.1\" width=\"544\" height=\"550\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-49.1.png 544w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-49.1-297x300.png 297w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42024\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-49.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 49.2\" width=\"567\" height=\"319\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-49.2.png 567w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-49.2-300x169.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 50.<br \/>\ny = -x<sup>2<\/sup> + 9x &#8211; 6<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-194287\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.2_50-246x300.png\" alt=\"Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.2_50\" width=\"246\" height=\"300\" \/><\/p>\n<p>Question 51.<br \/>\nf(x) = \\(\\frac{1}{2}\\)x<sup>2<\/sup> + 2x &#8211; 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42025\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-51.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 51.1\" width=\"503\" height=\"563\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-51.1.png 503w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-51.1-268x300.png 268w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42026\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-51.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 51.2\" width=\"581\" height=\"309\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-51.2.png 581w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-51.2-300x160.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 52.<br \/>\nf(x) = -3x<sup>2<\/sup> + 4x + 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-194288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.2_52-218x300.png\" alt=\"Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.2_52\" width=\"218\" height=\"300\" \/><\/p>\n<p>Question 53.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nAt a Civil War reenactment, a cannonball is fired into the air with an initial vertical velocity of 128 feet per second. The release point is 6 feet above the ground. The function h = -16t<sup>2<\/sup> + 128t + 6 represents the height h (in feet) of the cannonball after t seconds.<br \/>\na. Find the height of the cannonball each second after it is fired.<br \/>\nb. Use the results of part (a) to estimate when the height of the cannonball is 150 feet.<br \/>\nc. Using a graph, after how many seconds is the cannonball 150 feet above the ground?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35305\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-22.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 22\" width=\"159\" height=\"137\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42028\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-53.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 53.2\" width=\"565\" height=\"232\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-53.2.png 565w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-53.2-300x123.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou throw a softball straight up into the air with an initial vertical velocity of 40 feet per second. The release point is 5 feet above the ground. The function h = -16t<sup>2<\/sup> + 40t + 5 represents the height h (in feet) of the softball after t seconds.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35306\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 23\" width=\"131\" height=\"134\" \/><br \/>\na. Find the height of the softball each second after it is released.<br \/>\nAnswer:<br \/>\nb. Use the results of part (a) to estimate when the height of the softball is 15 feet.<br \/>\nc. Using a graph, after how many seconds is the softball 15 feet above the ground?<br \/>\nAnswer:<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong> In Exercises 55 and 56, use the given surface area S of the cylinder to find the radius r to the nearest tenth.<br \/>\nQuestion 55.<br \/>\nS = 225 ft<sup>2<\/sup><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35307\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-24.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 24\" width=\"137\" height=\"118\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42029\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 55\" width=\"573\" height=\"453\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-55.png 573w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-55-300x237.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 56.<br \/>\nS = 750 m<sup>2<\/sup><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35308\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 25\" width=\"135\" height=\"123\" \/><br \/>\nAnswer:<br \/>\nS = 750 m\u00b2<br \/>\nThe surface area of a cylinder (S) = 2\u03c0r\u00b2 + 2\u03c0rh<br \/>\nh = 13 m<br \/>\n750 = 2\u03c0r\u00b2 + 2\u03c0rh<br \/>\n750 = 2\u03c0r\u00b2 + 2\u03c0r (13)<br \/>\n750 = 2\u03c0r (r + 13)<br \/>\n375 = \u03c0r\u00b2 + 13\u03c0r<br \/>\n\u03c0r\u00b2 + 13\u03c0r &#8211; 375 = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112861\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-41.png\" alt=\"\" width=\"470\" height=\"470\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-41.png 470w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-41-300x300.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-41-150x150.png 150w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><br \/>\nThe radius of the given cylinder is 6.21<\/p>\n<p>Question 57.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to approximate zeros of a function when the zeros are not integers.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42030\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 57\" width=\"587\" height=\"167\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-57.png 587w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-57-300x85.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 58.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nConsider the graph shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35309\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-26.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 26\" width=\"175\" height=\"159\" \/><br \/>\na. How many solutions does the quadratic equation x<sup>2<\/sup> = -3x + 4 have? Explain.<br \/>\nAnswer:<br \/>\nx\u00b2 = -3x + 4<br \/>\nx\u00b2 + 3x &#8211; 4 = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112867\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-42.png\" alt=\"\" width=\"464\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-42.png 464w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-42-276x300.png 276w\" sizes=\"(max-width: 464px) 100vw, 464px\" \/><br \/>\nThe solutions of the given equation are -4 and 1<\/p>\n<p>b. Without graphing, describe what you know about the graph of y = x<sup>2<\/sup> + 3x &#8211; 4.<br \/>\nAnswer:<br \/>\ny = x\u00b2 + 3x &#8211; 4<br \/>\ny = 0<br \/>\nx\u00b2 + 3x &#8211; 4 = 0<br \/>\nx\u00b2 + 4x &#8211; x &#8211; 4 = 0<br \/>\nx (x + 4) &#8211; 1 (x + 4) = 0<br \/>\n(x &#8211; 1) (x + 4) = 0<br \/>\nx &#8211; 1 = 0 or x + 4 = 0<br \/>\nx = 1 or x = -4<\/p>\n<p>Question 59.<br \/>\n<strong>COMPARING METHODS<\/strong><br \/>\nExample 3 shows two methods for solving a quadratic equation. Which method do you prefer? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42031\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 59\" width=\"586\" height=\"60\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-59.png 586w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-59-300x31.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 60.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nHow many different parabolas have -2 and 2 as x-intercepts? Sketch examples of parabolas that have these two x-intercepts.<br \/>\nAnswer:<br \/>\nThere is only 1 parabola with -2 and 2 as x-intercepts<br \/>\nIf the equation has 2 solutions, then that equation will be a quadratic equation<br \/>\nThe equation with -2 and 2 as x-intercepts are:<br \/>\n(x+ 2) (x &#8211; 2) = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112869\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-43.png\" alt=\"\" width=\"470\" height=\"503\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-43.png 470w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-43-280x300.png 280w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/p>\n<p>Question 61.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nTo keep water off a road, the surface of the road is shaped like a parabola. A cross-section of the road is shown in the diagram. The surface of the road can be modeled by y = -0.0017x<sup>2<\/sup> + 0.041x, where x and y are measured in feet. Find the width of the road to the nearest tenth of a foot.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35310\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-27.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 27.1\" width=\"255\" height=\"100\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42033\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-61.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 61\" width=\"557\" height=\"269\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-61.png 557w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-61-300x145.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 62.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nA stream of water from a fire hose can be modeled by y = -0.003x<sup>2<\/sup> + 0.58x + 3,where x and y are measured in feet. A firefighter is standing 57 feet from a building and is holding the hose 3 feet above the ground. The bottom of a window of the building is 26 feet above the ground. Your friend claims the stream of water will pass through the window. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-194289 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.2_62.png\" alt=\"Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.2_62\" width=\"810\" height=\"626\" \/><br \/>\ny = -0.003x<sup>2<\/sup> + 0.58x + 3<br \/>\ny = -0.003(57)\u00b2 + 0.58(57) + 3<br \/>\ny = -9.747 + 33.06 + 3<br \/>\ny = 26.313<br \/>\nSo, 26.313 &gt; 26 and the stream of water passes through the window.<\/p>\n<p><strong>REASONING<\/strong> In Exercises 63\u201365, determine whether the statement is always, sometimes, or never true. Justify your answer.<br \/>\nQuestion 63.<br \/>\nThe graph of y = ax<sup>2<\/sup> + c has two x-intercepts when a is negative.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42034\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-63.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 63\" width=\"583\" height=\"145\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-63.png 583w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-63-300x75.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 64.<br \/>\nThe graph of y = ax<sup>2<\/sup> + c has no x-intercepts when a and c have the same sign.<br \/>\nAnswer:<br \/>\ny = ax\u00b2 + c<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112886\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-44.png\" alt=\"\" width=\"473\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-44.png 473w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-44-282x300.png 282w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><br \/>\nThe given statement is always false<\/p>\n<p>Question 65.<br \/>\nThe graph of y = ax<sup>2<\/sup> + bx + c has more than two x-intercepts when a \u2260 0.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42035\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-65.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 65\" width=\"528\" height=\"86\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-65.png 528w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-65-300x49.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p>Determine whether the table represents an exponential growth function, an exponential decay function, or neither. Explain.<br \/>\nQuestion 66.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35311\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 27\" width=\"213\" height=\"74\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-112892\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-45.png\" alt=\"\" width=\"476\" height=\"512\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-45.png 476w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-45-279x300.png 279w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><br \/>\nThe given table is exponential<\/p>\n<p>Question 67.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35312\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-28.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 28\" width=\"213\" height=\"72\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42036\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-67.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 67\" width=\"550\" height=\"258\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-67.png 550w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-67-300x141.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<h3><a id=\"Lesson_9.3_Solving_Quadratic_Equations_Using_Square_Roots\"><\/a>Lesson 9.3 Solving Quadratic Equations Using Square Roots<\/h3>\n<p><strong>Essential Question<\/strong><br \/>\nHow can you determine the number of solutions of a quadratic equation of the form ax<sup>2<\/sup> + c = 0?<br \/>\nAnswer:<br \/>\nQuadratic functions can have 0,1, or 2 solutions. This depends on the discriminant.<br \/>\nx = (-b \u00b1\\(\\sqrt{ b\u00b2 &#8211; 4ac}\\)\/2a<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>The Number of Solutions of ax<sup>2<\/sup> + c = 0<br \/>\nWork with a partner. Solve each equation by graphing. Explain how the number of solutions of ax<sup>2<\/sup> + c = 0 relates to the graph of y = ax<sup>2<\/sup> + c.<br \/>\na. x<sup>2<\/sup> &#8211; 4 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 4 = 0<br \/>\nx\u00b2 &#8211; 4 + 4 = 0 + 4<br \/>\nx\u00b2 = 4<br \/>\n\u221ax\u00b2 = \u221a4<br \/>\nx = 2 or x = -2<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113193\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-46.png\" alt=\"\" width=\"468\" height=\"500\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-46.png 468w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-46-281x300.png 281w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><br \/>\nThere are 2 real solutions for the given equation i.e., -2 and 2<\/p>\n<p>b. 2x<sup>2<\/sup> + 5 = 0<br \/>\nAnswer:<br \/>\n2x\u00b2 + 5 = 0<br \/>\n2x\u00b2 + 5 &#8211; 5 = 0 &#8211; 5<br \/>\n2x\u00b2 = -5<br \/>\nx\u00b2 = &#8211;\\(\\frac{5}{2}\\)<br \/>\n\u221ax\u00b2 = -\u221a\\(\\frac{5}{2}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113195\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-47.png\" alt=\"\" width=\"473\" height=\"510\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-47.png 473w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-47-278x300.png 278w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><br \/>\nThe given equation does not have any real solutions.<\/p>\n<p>c. x<sup>2<\/sup> = 0<br \/>\nAnswer:<br \/>\nx\u00b2 = 0<br \/>\nx = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113199\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-48.png\" alt=\"\" width=\"482\" height=\"502\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-48.png 482w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-48-288x300.png 288w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><br \/>\nThe given equation has only one solution i.e., 0<\/p>\n<p>d. x<sup>2<\/sup> &#8211; 5 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 5 = 0<br \/>\nx\u00b2 &#8211; 5 + 5 = 0 + 5<br \/>\nx\u00b2 = 5<br \/>\n\u221ax\u00b2 = \u221a5<br \/>\nx = \u221a5 or x = -\u221a5<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113201\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-49.png\" alt=\"\" width=\"475\" height=\"501\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-49.png 475w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-49-284x300.png 284w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><br \/>\nThere are 2 real solutions i.e., \u221a5 and -\u221a5<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Estimating Solutions<br \/>\nWork with a partner. Complete each table. Use the completed tables to estimate the solutions of x<sup>2<\/sup> &#8211; 5 = 0. Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35313\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 1\" width=\"448\" height=\"195\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-1.png 448w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-1-300x131.png 300w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/><br \/>\nAnswer:<br \/>\nThe completed tables are:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113234\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9.jpg\" alt=\"\" width=\"450\" height=\"190\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9.jpg 450w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-300x127.jpg 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><br \/>\nx\u00b2 &#8211; 5 = 0<br \/>\nThe solutions of the given equation are: 2.24 and -2.24<\/p>\n<p><strong>EXPLORATION 3<\/strong><\/p>\n<p>Using Technology to Estimate Solutions<br \/>\nWork with a partner. Two equations are equivalent when they have the same solutions.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35314\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-2.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 2\" width=\"221\" height=\"208\" \/><br \/>\na. Are the equations x<sup>2<\/sup> &#8211; 5 = 0 and x<sup>2<\/sup> = 5 equivalent? Explain your reasoning<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 5 = 0<br \/>\nx\u00b2 &#8211; 5 + 5= 0 + 5<br \/>\nx\u00b2= 5<br \/>\nx\u00b2 &#8211; 5 and x\u00b2 = 5 are equivalent<\/p>\n<p>b. Use the square root key on a calculator to estimate the solutions of x<sup>2<\/sup> &#8211; 5 = 0. Describe the accuracy of your estimates in Exploration 2.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113236\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-50.png\" alt=\"\" width=\"374\" height=\"396\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-50.png 374w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-50-283x300.png 283w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><\/p>\n<p>c. Write the exact solutions of x<sup>2<\/sup> &#8211; 5 = 0.<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 5 = 0<br \/>\nThe exact solutions of the given equation are: 2.24 and -2.24<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 4.<br \/>\nHow can you determine the number of solutions of a quadratic equation of the form ax<sup>2<\/sup> + c = 0?<br \/>\nAnswer:<br \/>\nQuadratic functions can have 0,1, or 2 solutions. This depends on the discriminant.<br \/>\nx = (-b \u00b1\\(\\sqrt{ b\u00b2 &#8211; 4ac}\\) \/ 2a<\/p>\n<p>Question 5.<br \/>\nWrite the exact solutions of each equation. Then use a calculator to estimate the solutions.<br \/>\na. x<sup>2<\/sup> &#8211; 2 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113238\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-51.png\" alt=\"\" width=\"278\" height=\"241\" \/><\/p>\n<p>b. 3x<sup>2<\/sup> &#8211; 18 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113252\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-52.png\" alt=\"\" width=\"305\" height=\"388\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-52.png 305w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-52-236x300.png 236w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\nc. x<sup>2<\/sup> &#8211; 8 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 8 = 0<br \/>\nx\u00b2 &#8211; 8+ 8 = 0 + 8<br \/>\nx\u00b2 = 8<br \/>\n\u221ax\u00b2 = \u221a8<br \/>\nx = \u221a8 or x = -\u221a8<br \/>\nThe value of \u221a8 is: 2.83<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the equation using square roots.<\/strong><br \/>\nQuestion 1.<br \/>\n-3x<sup>2<\/sup> = -75<br \/>\nAnswer:<br \/>\n-3x\u00b2 = -75<br \/>\n3x\u00b2 = 75<br \/>\nx\u00b2 = \\(\\frac{75}{3}\\)<br \/>\nx\u00b2 = 25<br \/>\n\u221ax\u00b2 = \u221a25<br \/>\nx = 5 or x = -5<\/p>\n<p>Question 2.<br \/>\nx<sup>2<\/sup> + 12 = 10<br \/>\nAnswer:<br \/>\nx\u00b2 + 12 = 10<br \/>\nx\u00b2 = 10 &#8211; 12<br \/>\nx\u00b2 = -2<br \/>\n\u221ax\u00b2 = \u221a-2<br \/>\nThe given equation does not have any real solutions<\/p>\n<p>Question 3.<br \/>\n4x<sup>2<\/sup> &#8211; 15 = -15<br \/>\nAnswer:<br \/>\n4x\u00b2 &#8211; 15 = -15<br \/>\n4x\u00b2 = -15 + 15<br \/>\n4x\u00b2 = 0<br \/>\nx\u00b2 = 0<br \/>\n\u221ax\u00b2 = \u221a0<br \/>\nx = 0<\/p>\n<p>Question 4.<br \/>\n(x + 7)<sup>2<\/sup> = 0<br \/>\nAnswer:<br \/>\n(x + 7)\u00b2 = 0<br \/>\n\u221a(x + 7)\u00b2 = \u221a0<br \/>\nx + 7 = 0<br \/>\nx = 0 &#8211; 7<br \/>\nx = -7<\/p>\n<p>Question 5.<br \/>\n4(x &#8211; 3)<sup>2<\/sup> = 9<br \/>\nAnswer:<br \/>\n4 (x &#8211; 3)\u00b2 = 9<br \/>\n(x &#8211; 3)\u00b2 = \\(\\frac{9}{4}\\)<br \/>\n\u221a(x &#8211; 3)\u00b2 = \u221a\\(\\frac{9}{4}\\)<br \/>\nx &#8211; 3 = \\(\\frac{3}{2}\\) or x &#8211; 3 = &#8211;\\(\\frac{3}{2}\\)<br \/>\nx = \\(\\frac{3}{2}\\) + 3 or x = &#8211;\\(\\frac{3}{2}\\) + 3<br \/>\nx = \\(\\frac{9}{2}\\) or x = \\(\\frac{3}{2}\\)]<\/p>\n<p>Question 6.<br \/>\n(2x + 1)<sup>2<\/sup> = 36<br \/>\nAnswer:<br \/>\n(2x + 1)\u00b2 = 36<br \/>\n\u221a(2x + 1)\u00b2 = \u221a36<br \/>\n2x + 1 = 6 or 2x + 1 = -6<br \/>\n2x = 6 &#8211; 1 or 2x = -6 &#8211; 1<br \/>\n2x = 5 or 2x = -7<br \/>\nx = \\(\\frac{5}{2}\\) or x = &#8211;\\(\\frac{7}{2}\\)<\/p>\n<p><strong>Solve the equation using square roots. Round your solutions to the nearest hundredth.<\/strong><br \/>\nQuestion 7.<br \/>\nx<sup>2<\/sup> + 8 = 19<br \/>\nAnswer:<br \/>\nx\u00b2 + 8 = 19<br \/>\nx\u00b2 + 8 &#8211; 8 = 19 &#8211; 8<br \/>\nx\u00b2 = 11<br \/>\n\u221ax\u00b2 = \u221a11<br \/>\nx = \u221a11 or x = -\u221a11<br \/>\nThe value of \u221a11 is: 3.31<\/p>\n<p>Question 8.<br \/>\n5x<sup>2<\/sup> &#8211; 2 = 0<br \/>\nAnswer:<br \/>\n5x\u00b2 &#8211; 2 = 0<br \/>\n5x\u00b2 &#8211; 2 + 2 = 0 + 2<br \/>\n5x\u00b2 = 2<br \/>\nx\u00b2 = \\(\\frac{2}{5}\\)<br \/>\n\u221ax\u00b2 = \u221a\\(\\frac{2}{5}\\)<br \/>\nx = \u221a\\(\\frac{2}{5}\\) or x = -\u221a\\(\\frac{2}{5}\\)<br \/>\nThe value of \\(\\frac{2}{5}\\) is: 0.40<\/p>\n<p>Question 9.<br \/>\n3x<sup>2<\/sup> &#8211; 30 = 4<br \/>\nAnswer:<br \/>\n3x\u00b2 &#8211; 30 = 4<br \/>\n3x\u00b2 = 4 + 30<br \/>\n3x\u00b2= 34<br \/>\nx\u00b2 = \\(\\frac{34}{3}\\)<br \/>\n\u221ax\u00b2 = \u221a\\(\\frac{34}{3}\\)<br \/>\nx = \u221a\\(\\frac{34}{3}\\) or x = -\u221a\\(\\frac{34}{3}\\)<br \/>\nThe value of \\(\\frac{34}{3}\\) is: 11.33<\/p>\n<p>Question 10.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 4, the volume of the tank is 315 cubic feet. Find the length and width of the tank.<br \/>\nAnswer:<br \/>\nA touch tank has a height of 3 feet and its length is 3 times its width<br \/>\nThe volume of the tank (V) = l \u00d7 w \u00d7 h<br \/>\n315 = 3w (w) (3)<br \/>\n315 = 9w\u00b2<br \/>\nw\u00b2 = \\(\\frac{315}{9}\\)<br \/>\nw\u00b2 = 35<br \/>\n\u221aw\u00b2 = \u221a35<br \/>\nw = \u221a35 or w = -\u221a35<br \/>\nThe volume won&#8217;t be negative<br \/>\nThe value of \u221a35 is: 5.91<br \/>\nThe width of the tank is: 5.91<br \/>\nThe length of the tank is: 3 (5.91) = 17.74<br \/>\nThe length of the tank is: 17.74<br \/>\nThe width of the tank is 5.91<\/p>\n<p>Question 11.<br \/>\nThe surface area S of a sphere with radius r is given by the formula S = 4\u03c0r<sup>2<\/sup>. Solve the formula for r. Then find the radius of a globe with a surface area of 804 square inches.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35315\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 3\" width=\"183\" height=\"125\" \/><br \/>\nAnswer:<br \/>\nThe surface area S of a sphere is given by the formula<br \/>\nS = 4\u03c0r\u00b2<br \/>\nr\u00b2 = \\(\\frac{S}{4\u03c0}\\)<br \/>\n\u221ar\u00b2 = \u221a\\(\\frac{S}{4\u03c0}\\)<br \/>\nr = \u221a\\(\\frac{S}{4\u03c0}\\) or r = -\u221a\\(\\frac{S}{4\u03c0}\\)<br \/>\nThe surface area S of the sphere won&#8217;t take negative values<br \/>\nr = \u221a\\(\\frac{S}{4\u03c0}\\)<br \/>\nr = \u221a\\(\\frac{804}{4\u03c0}\\)<br \/>\nr = 64.01 units<br \/>\nThe radius of a globe with a surface area of 804 sq. units is: 64.01 units<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Using_Square_Roots_9.3_Exercises\"><\/a>Solving Quadratic Equations Using Square Roots 9.3 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe equation x<sup>2<\/sup> = d has ____ real solutions when d &gt; 0.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42037\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 1\" width=\"525\" height=\"37\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-1.png 525w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-1-300x21.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35316\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-4.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 4\" width=\"559\" height=\"96\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-4.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-4-300x52.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><br \/>\nAnswer:<br \/>\na, b, and d are the same because in these 3 equations,<br \/>\nx\u00b2 = 144<br \/>\nBut, in d,<br \/>\nx\u00b2 = -144<br \/>\nThe equations a, b, and d are the same whereas the equation c is different<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20138, determine the number of real solutions of the equation. Then solve the equation using square roots.<\/strong><br \/>\nQuestion 3.<br \/>\nx<sup>2<\/sup> = 25<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42038\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 3\" width=\"481\" height=\"169\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-3.png 481w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-3-300x105.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>Question 4.<br \/>\nx<sup>2<\/sup> = -36<br \/>\nAnswer:<br \/>\nx\u00b2 = -36<br \/>\n\u221ax\u00b2 = \u221a-36<br \/>\nx = \u221a-36<br \/>\nThere are no real solutions for the given equation<\/p>\n<p>Question 5.<br \/>\nx<sup>2<\/sup> = -21<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42039\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-5.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 5\" width=\"503\" height=\"31\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-5.png 503w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-5-300x18.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/p>\n<p>Question 6.<br \/>\nx<sup>2<\/sup> = 400<br \/>\nAnswer:<br \/>\nx\u00b2 = 400<br \/>\n\u221ax\u00b2 = \u221a400<br \/>\nx = 20 or x = -20<br \/>\nThere are 2 real solutions for the given equation i.e., 20 and -20<\/p>\n<p>Question 7.<br \/>\nx<sup>2<\/sup> = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42040\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-7.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 7\" width=\"404\" height=\"173\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-7.png 404w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-7-300x128.png 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><\/p>\n<p>Question 8.<br \/>\nx<sup>2<\/sup> = 169<br \/>\nAnswer:<br \/>\nx\u00b2 = 169<br \/>\n\u221ax\u00b2 = \u221a169<br \/>\nx = 13 or x = -13<br \/>\nThere are 2 real solutions for the given equation i.e., 13 and -13<\/p>\n<p><strong>In Exercises 9\u201318, solve the equation using square roots.<\/strong><br \/>\nQuestion 9.<br \/>\nx<sup>2<\/sup> &#8211; 16 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42041\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-9.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 9\" width=\"363\" height=\"206\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-9.png 363w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-9-300x170.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 10.<br \/>\nx<sup>2<\/sup> + 6 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 + 6 = 0<br \/>\nx\u00b2 + 6 &#8211; 6 = 0 &#8211; 6<br \/>\nx\u00b2 = -6<br \/>\n\u221ax\u00b2 = \u221a-6<br \/>\nx = \u221a-6<br \/>\nThere are no real solutions for the given equation<\/p>\n<p>Question 11.<br \/>\n3x<sup>2<\/sup> + 12 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42042\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-11.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 11\" width=\"516\" height=\"257\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-11.png 516w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-11-300x149.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/p>\n<p>Question 12.<br \/>\nx<sup>2<\/sup> &#8211; 55 = 26<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 55 = 26<br \/>\nx\u00b2 &#8211; 55 + 55 = 26 + 55<br \/>\nx\u00b2 = 81<br \/>\n\u221ax\u00b2 = \u221a81<br \/>\nx = 9 or x = -9<\/p>\n<p>Question 13.<br \/>\n2x<sup>2<\/sup> &#8211; 98 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42043\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-13.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 13\" width=\"343\" height=\"295\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-13.png 343w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-13-300x258.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/p>\n<p>Question 14.<br \/>\n-x<sup>2<\/sup> + 9 = 9<br \/>\nAnswer:<br \/>\n-x\u00b2 + 9 = 9<br \/>\n-x\u00b2 + 9 &#8211; 9 = 9 &#8211; 9<br \/>\n-x\u00b2 = 0<br \/>\nx\u00b2 = 0<br \/>\n\u221ax\u00b2 = \u221a0<br \/>\nx = 0<\/p>\n<p>Question 15.<br \/>\n-3x<sup>2<\/sup> &#8211; 5 = -5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42044\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-15.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 15\" width=\"263\" height=\"313\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-15.png 263w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-15-252x300.png 252w\" sizes=\"(max-width: 263px) 100vw, 263px\" \/><\/p>\n<p>Question 16.<br \/>\n4x<sup>2<\/sup> &#8211; 371 = 29<br \/>\nAnswer:<br \/>\n4x\u00b2 &#8211; 371 = 29<br \/>\n4x\u00b2 &#8211; 371 + 371 = 29 + 371<br \/>\n4x\u00b2 = 400<br \/>\nx\u00b2 = \\(\\frac{400}{4}\\)<br \/>\nx\u00b2 = 100<br \/>\n\u221ax\u00b2 = \u221a100<br \/>\nx = 10 or x = -10<\/p>\n<p>Question 17.<br \/>\n4x<sup>2<\/sup> + 10 = 11<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42045\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-17.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 17\" width=\"342\" height=\"408\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-17.png 342w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-17-251x300.png 251w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/p>\n<p>Question 18.<br \/>\n9x<sup>2<\/sup> &#8211; 35 = 14<br \/>\nAnswer:<br \/>\n9x\u00b2 &#8211; 35 = 14<br \/>\n9x\u00b2 &#8211; 35 + 5 = 14 + 35<br \/>\n9x\u00b2 = 49<br \/>\nx\u00b2 = \\(\\frac{49}{9}\\)<br \/>\n\u221ax\u00b2 = \u221a\\(\\frac{49}{9}\\)<br \/>\nx = \\(\\frac{7}{3}\\) or x = &#8211;\\(\\frac{7}{3}\\)<\/p>\n<p><strong>In Exercises 19\u201324, solve the equation using square roots.<\/strong><br \/>\nQuestion 19.<br \/>\n(x + 3)<sup>2<\/sup> = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42046\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-19.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 19\" width=\"273\" height=\"221\" \/><\/p>\n<p>Question 20.<br \/>\n(x &#8211; 1)<sup>2<\/sup> = 4<br \/>\nAnswer:<br \/>\n(x &#8211; 1)\u00b2 = 4<br \/>\n\u221a(x &#8211; 1)\u00b2 = \u221a4<br \/>\nx &#8211; 1 = 2 or x &#8211; 1 = -2<br \/>\nx = 2 + 1 or x = -2 + 1<br \/>\nx = 3 or x = -1<\/p>\n<p>Question 21.<br \/>\n(2x &#8211; 1)<sup>2<\/sup> = 81<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42047\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-21.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 21\" width=\"416\" height=\"475\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-21.png 416w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-21-263x300.png 263w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><\/p>\n<p>Question 22.<br \/>\n(4x + 5)<sup>2<\/sup> = 9<br \/>\nAnswer:<br \/>\n(4x + 5)\u00b2 = 9<br \/>\n\u221a(4x + 5)\u00b2 = \u221a9<br \/>\n4x + 5 = 3 or 4x + 5 = -3<br \/>\n4x = 3 &#8211; 5 or 4x = -3 &#8211; 5<br \/>\n4x = -2 or 4x = -8<br \/>\nx = \\(\\frac{-2}{4}\\) or x = \\(\\frac{-8}{4}\\)<br \/>\nx = &#8211;\\(\\frac{1}{2}\\) or x = -2<\/p>\n<p>Question 23.<br \/>\n9(x + 1)<sup>2<\/sup> = 16<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42048\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-23.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 23\" width=\"576\" height=\"415\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-23.png 576w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-23-300x216.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 24.<br \/>\n4(x &#8211; 2)<sup>2<\/sup> = 25<br \/>\nAnswer:<br \/>\n4 (x &#8211; 2)\u00b2 = 25<br \/>\n(x &#8211; 2)\u00b2 = \\(\\frac{25}{4}\\)<br \/>\n\u221a(x &#8211; 2)\u00b2 = \u221a\\(\\frac{25}{4}\\)<br \/>\nx &#8211; 2 = \\(\\frac{5}{2}\\) or x &#8211; 2 = &#8211;\\(\\frac{5}{2}\\)<br \/>\nx= \\(\\frac{5}{2}\\) + 2 or x = &#8211;\\(\\frac{5}{2}\\) + 2<br \/>\nx = \\(\\frac{9}{2}\\) or x = &#8211;\\(\\frac{1}{2}\\)<\/p>\n<p><strong>In Exercises 25\u201330, solve the equation using square roots. Round your solutions to the nearest hundredth.<\/strong><br \/>\nQuestion 25.<br \/>\nx<sup>2<\/sup> + 6 = 13<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42049\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-25.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 25\" width=\"408\" height=\"328\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-25.png 408w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-25-300x241.png 300w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><\/p>\n<p>Question 26.<br \/>\nx<sup>2<\/sup> + 11 = 24<br \/>\nAnswer:<br \/>\nx\u00b2 + 11 = 24<br \/>\nx\u00b2 + 11 &#8211; 11 = 24 &#8211; 11<br \/>\nx\u00b2 = 13<br \/>\n\u221ax\u00b2 = \u221a13<br \/>\nx = \u221a13 or x = -\u221a13<br \/>\nThe solutions of the given equation are: 3.60 and -3.60<\/p>\n<p>Question 27.<br \/>\n2x<sup>2<\/sup> &#8211; 9 = 11<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42050\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-27.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 27\" width=\"400\" height=\"315\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-27.png 400w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-27-300x236.png 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>Question 28.<br \/>\n5x<sup>2<\/sup> + 2 = 6<br \/>\nAnswer:<br \/>\n5x\u00b2 + 2 = 6<br \/>\n5x\u00b2 + 2 &#8211; 2 = 6 &#8211; 2<br \/>\n5x\u00b2 = 4<br \/>\nx\u00b2 = \\(\\frac{4}{5}\\)<br \/>\n\u221ax\u00b2 = \u221a\\(\\frac{4}{5}\\)<br \/>\nx = \\(\\frac{2}{\u221a5}\\) or x = &#8211;\\(\\frac{2}{\u221a5}\\)<br \/>\n\\(\\frac{2}{\u221a5}\\) = 0.89<br \/>\nThe solutions of the given equation are 0.89 and -0.89<\/p>\n<p>Question 29.<br \/>\n-21 = 15 &#8211; 2x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42051\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-29.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 29\" width=\"401\" height=\"399\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-29.png 401w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-29-300x300.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-29-150x150.png 150w\" sizes=\"(max-width: 401px) 100vw, 401px\" \/><\/p>\n<p>Question 30.<br \/>\n2 = 4x<sup>2<\/sup> &#8211; 5<br \/>\nAnswer:<br \/>\n2 = 4x\u00b2 &#8211; 5<br \/>\n2 + 5 = 4x\u00b2 &#8211; 5 + 5<br \/>\n7 = 4x\u00b2<br \/>\nx\u00b2 = \\(\\frac{7}{4}\\)<br \/>\n\u221ax\u00b2 = \u221a\\(\\frac{7}{4}\\)<br \/>\nx = \u221a\\(\\frac{7}{4}\\) or x = -\u221a\\(\\frac{7}{4}\\)<br \/>\nThe solutions of the given equation are 1.32 and -1.32<\/p>\n<p>Question 31.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving the equation 2x<sup>2<\/sup> &#8211; 33 = 39 using square roots.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35317\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-5.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 5\" width=\"323\" height=\"141\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-5.png 323w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-5-300x131.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42052\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-31.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 31\" width=\"556\" height=\"329\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-31.png 556w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-31-300x178.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nAn in-ground pond has the shape of a rectangular prism. The pond has a depth of 24 inches and a volume of 72,000 cubic inches. The length of the pond is two times its width. Find the length and width of the pond.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35318\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-6.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 6\" width=\"274\" height=\"171\" \/><br \/>\nAnswer:<br \/>\nThe volume of a rectangular prism (V) = l \u00d7 w \u00d7 h<br \/>\nIt is also given that the length of the pond is two times its width<br \/>\nV = (2w) \u00d7 w \u00d7 h<br \/>\n72,000 = 2w\u00b2 \u00d7 24<br \/>\n2w\u00b2 = \\(\\frac{72,000}{24}\\)<br \/>\n2w\u00b2 = 3,000<br \/>\nw\u00b2 = \\(\\frac{3,000}{2}\\)<br \/>\nw\u00b2 = 1,500<br \/>\n\u221aw\u00b2 = \u221a1,500<br \/>\nw = \u221a1,500 or w = -\u221a1,500<br \/>\nw = \u221a1,500<br \/>\nThe width of the rectangular prism = 38.72 inches<br \/>\nThe length of the rectangular prism = 2 (38.72) = 77.45 inches<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA person sitting in the top row of the bleachers at a sporting event drops a pair of sunglasses from a height of 24 feet. The function h = -16x<sup>2<\/sup> + 24 represents the height h (in feet) of the sunglasses after x seconds. How long does it take the sunglasses to hit the ground?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42053\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-33.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 33\" width=\"530\" height=\"592\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-33.png 530w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-33-269x300.png 269w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says that the solution of the equation x<sup>2<\/sup> + 4 = 0 is x = 0. Your cousin says that the equation has no real solutions. Who is correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\nx\u00b2 + 4 = 0<br \/>\nx\u00b2 + 4 &#8211; 4 = 0- 4<br \/>\nx\u00b2 = -4<br \/>\nThe square of a real number can&#8217;t take any negative numbers<br \/>\nThere are no real solutions for the given equation<br \/>\nYour cousin is correct<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe design of a square rug for your living room is shown. You want the area of the inner square to be 25% of the total area of the rug. Find the side length x of the inner square.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35319\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-7.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 7\" width=\"169\" height=\"174\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42054\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-35.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 35\" width=\"571\" height=\"229\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-35.png 571w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-35-300x120.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe area A of a circle with radius r is given by the formula A = \u03c0r<sup>2<\/sup>.<br \/>\na. Solve the formula for r.<br \/>\nAnswer:<br \/>\nA = \u03c0r\u00b2<br \/>\nr\u00b2 = \\(\\frac{A}{\u03c0}\\)<br \/>\n\u221ar\u00b2 = \u221a\\(\\frac{A}{\u03c0}\\)<br \/>\nr = \u221a\\(\\frac{A}{\u03c0}\\) or r = -\u221a\\(\\frac{A}{\u03c0}\\)<br \/>\nThe radius of the circle won&#8217;t take any negative values<br \/>\nr = \u221a\\(\\frac{A}{\u03c0}\\)<\/p>\n<p>b. Use the formula from part (a) to find the radius of each circle.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35320\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-8.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 8\" width=\"309\" height=\"122\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-8.png 309w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-8-300x118.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nAnswer:<br \/>\nr = \u221a\\(\\frac{A}{\u03c0}\\)<br \/>\nFor A = 113ft\u00b2,<br \/>\nr = \u221a\\(\\frac{113}{\u03c0}\\)<br \/>\nr = 5.99ft<br \/>\nFor A = 810 in.\u00b2,<br \/>\nr = \u221a\\(\\frac{1810}{\u03c0}\\)<br \/>\nr = 24 in.<br \/>\nFor A = 531m\u00b2,<br \/>\nr = \u221a\\(\\frac{531}{\u03c0}\\)<br \/>\nr = 13m<\/p>\n<p>c. Explain why it is beneficial to solve the formula for r before finding the radius.<br \/>\nAnswer:<br \/>\nIt is beneficial to solve the formula for r before finding the radius because the formula for r is complicated due to the square root and it will become easy if we simplified the formula for r before finding the value of r<\/p>\n<p>Question 37.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow can you approximate the roots of a quadratic equation when the roots are not integers?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42055\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-37.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 37\" width=\"514\" height=\"57\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-37.png 514w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-37-300x33.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>WRITING<\/strong><br \/>\nGiven the equation ax<sup>2<\/sup> + c = 0, describe the values of a and c so the equation has the following number of solutions.<br \/>\na. two real solutions<br \/>\nb. one real solution<br \/>\nc. no real solutions<br \/>\nAnswer:<br \/>\nax\u00b2 + c = 0<br \/>\nax\u00b2\u00a0 + c &#8211; c = 0 &#8211; c<br \/>\nax\u00b2 = -c<br \/>\na. Two real solutions<br \/>\nFor the equations to have 2 real solutions,<br \/>\na &#8212;-&gt; Positive<br \/>\nc &#8212;&#8211;&gt; Negative<br \/>\nb. One real solution<br \/>\nFor the equation to have 1 real solution,<br \/>\na &#8212;&#8211;&gt; Positive<br \/>\nc &#8212;&#8212;&gt; Zero<br \/>\nc. No real solutions<br \/>\nFor the equation to have no real solutions,<br \/>\na &#8212;&#8211;&gt; Positive<br \/>\nc &#8212;&#8211;&gt; Positive<\/p>\n<p>Question 39.<br \/>\n<strong>REASONING<\/strong><br \/>\nWithout graphing, where do the graphs of y = x<sup>2<\/sup> and y = 9 intersect? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42056\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-39.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 39\" width=\"499\" height=\"84\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-39.png 499w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-39-300x51.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph represents the function f(x) = (x &#8211; 1)<sup>2<\/sup>. How many solutions does the equation (x &#8211; 1)<sup>2<\/sup> = 0 have? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35321\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-9.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 9\" width=\"176\" height=\"171\" \/><br \/>\nAnswer:<br \/>\nf (x) = (x &#8211; 1)\u00b2<br \/>\nf (x) = 0<br \/>\n(x &#8211; 1)\u00b2 = 0<br \/>\n\u221a(x &#8211; 1)\u00b2 = \u221a0<br \/>\nx &#8211; 1 = 0<br \/>\nx = 0 + 1<br \/>\nx = 1<\/p>\n<p>Question 41.<br \/>\n<strong>REASONING<\/strong><br \/>\nSolve x<sup>2<\/sup> = 1.44 without using a calculator. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42057\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-41.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 41\" width=\"501\" height=\"195\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-41.png 501w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-41-300x117.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nThe quadratic equation ax<sup>2<\/sup> + bx + c = 0 can be rewritten in the following form. \\(\\left(x+\\frac{b}{2 a}\\right)^{2}=\\frac{b^{2}-4 a c}{4 a^{2}}\\) Use this form to write the solutions of the equation.<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>REASONING<\/strong><br \/>\nAn equation of the graph shown is y = \\(\\frac{1}{2}\\)(x &#8211; 2)<sup>2<\/sup> + 1. Two points on the parabola have y-coordinates of 9. Find the x-coordinates of these points.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35322\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-10.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 10\" width=\"161\" height=\"123\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42058\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-43.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 43\" width=\"559\" height=\"381\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-43.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-43-300x204.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nSolve each equation without graphing.<br \/>\na. x<sup>2<\/sup> &#8211; 12x + 36 = 64<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113735\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-53.png\" alt=\"\" width=\"351\" height=\"320\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-53.png 351w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-53-300x274.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><\/p>\n<p>b. x<sup>2<\/sup> + 14x + 49 = 16<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-113737\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-54.png\" alt=\"\" width=\"351\" height=\"314\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-54.png 351w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-54-300x268.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Factor the polynomial.<\/strong><br \/>\nQuestion 45.<br \/>\nx<sup>2<\/sup> + 8x + 16<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42059\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-45.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 45\" width=\"337\" height=\"65\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-45.png 337w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-45-300x58.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/p>\n<p>Question 46.<br \/>\nx<sup>2<\/sup> &#8211; 4x + 4<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 4x + 4<br \/>\n= x\u00b2 &#8211; 2x &#8211; 2x + 4<br \/>\n= x (x &#8211; 2) &#8211; 2 (x &#8211; 2)<br \/>\n= (x &#8211; 2) ( x &#8211; 2)<br \/>\n= (x &#8211; 2)\u00b2<\/p>\n<p>Question 47.<br \/>\nx<sup>2<\/sup> &#8211; 14x + 49<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42060\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-47.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 47\" width=\"334\" height=\"67\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-47.png 334w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-47-300x60.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/p>\n<p>Question 48.<br \/>\nx<sup>2<\/sup> + 18x + 81<br \/>\nAnswer:<br \/>\nx\u00b2 + 18x + 81<br \/>\n= x\u00b2 + 9x + 9x + 81<br \/>\n= x (x + 9) + 9 (x + 9)<br \/>\n= (x + 9) (x + 9)<br \/>\n= (x + 9)\u00b2<\/p>\n<p>Question 49.<br \/>\nx<sup>2<\/sup> + 12x + 36<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42061\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-49.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 49\" width=\"342\" height=\"70\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-49.png 342w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-49-300x61.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/p>\n<p>Question 50.<br \/>\nx<sup>2<\/sup> &#8211; 22x + 121<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 22x + 121<br \/>\n= x\u00b2 &#8211; 11x &#8211; 11x + 121<br \/>\n= x (x &#8211; 11) &#8211; 11 (x &#8211; 11)<br \/>\n= (x &#8211; 11) (x &#8211; 11)<br \/>\n= (x &#8211; 11)\u00b2<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Study_Skills:_Keeping_a_Positive_Attitude\"><\/a>Solving Quadratic Equations Study Skills: Keeping a Positive Attitude<\/h3>\n<p><strong>9.1\u20139.3 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35323\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-11.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 11\" width=\"510\" height=\"86\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-11.png 510w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-11-300x51.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p><strong>Core Concepts<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35324\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-12.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 12\" width=\"621\" height=\"222\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-12.png 621w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-12-300x107.png 300w\" sizes=\"(max-width: 621px) 100vw, 621px\" \/><\/p>\n<p><strong>Mathematical Practices<\/strong><\/p>\n<p>Question 1.<br \/>\nFor each part of Exercise 100 on page 488 that is sometimes true, list all examples and counterexamples from the table that represent the sum or product being described.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nWhich Examples can you use to help you solve Exercise 54 on page 496?<br \/>\nAnswer:<br \/>\nYou can use Example 6 on page 493 to solve Exercise 54 on page 496<\/p>\n<p>Question 3.<br \/>\nDescribe how solving a simpler equation can help you solve the equation in Exercise 41 on page 502.<br \/>\nAnswer:<br \/>\nThe equation in Exercise 41 on page 502 is in the form of:<br \/>\nx\u00b2 &#8211; a = 0<br \/>\nIf d&gt; 0 i.e., the square is a positive number, then the only square root exists<br \/>\nWe can solve Exercise 41 on page 502<\/p>\n<p><strong>Study Skills: Keeping a Positive Attitude<\/strong><\/p>\n<p>Do you ever feel frustrated or overwhelmed by math? You\u2019re not alone. Just take a deep breath and assess the situation. Try to find a productive study environment, review your notes and the examples in the textbook, and ask your teacher or friends for help.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35325\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-13.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 13\" width=\"363\" height=\"272\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-13.png 363w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-13-300x225.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<h3><a id=\"Solving_Quadratic_Equations_9.1_\u2013_9.3_Quiz\"><\/a>Solving Quadratic Equations 9.1 \u2013 9.3 Quiz<\/h3>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\sqrt{112 x^{3}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{112 x^{3}}\\)<br \/>\n= \\(\\sqrt{{112 x^{2}}\\cdot x}\\)<br \/>\n= \\(\\sqrt{16 \u00d7 7 x^{2}}\\) \u22c5 \\(\\sqrt{x}\\)<br \/>\n= 4x \\(\\sqrt{7x}\\)<\/p>\n<p>Question 2.<br \/>\n\\(\\sqrt{\\frac{18}{81}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{\\frac{18}{81}}\\)<br \/>\n= \\(\\sqrt{\\frac{18}{81}}\\)<br \/>\n= \\(\\frac{\\sqrt{18}}{\\sqrt{81}}\\)<br \/>\n= \\(\\frac{3\\sqrt{2}}{9}\\)<br \/>\n= \\(\\frac{\\sqrt{2}}{3}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt[3]{-625}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt[3]{-625}\\)<br \/>\n= \\(\\sqrt[3]{-625}{1}\\)<br \/>\n= \\(\\sqrt[3]{-625}\\) \u22c5 \\(\\sqrt[3]{1}\\)<br \/>\n= \\(\\sqrt[3]{-125 \u00d7 5}\\)<br \/>\n= \\(\\sqrt[3]{-125}\\) \u22c5 \\(\\sqrt[3]{5}\\)<br \/>\n= -5\\(\\sqrt[3]{5}\\)<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{12}{\\sqrt{32}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{12}{\\sqrt{32}}\\)<br \/>\nTo rationalize the denominator, multiply and divide the given fraction with \\(\\sqrt{32}\\)<br \/>\n= \\(\\frac{12}{\\sqrt{32}}\\) \u00d7 (\\(\\sqrt{32}\\) \/ \\(\\sqrt{32}\\))<br \/>\n= \\(12\\sqrt{32}\\) \/ (\\(\\sqrt{32}\\) \u00d7 \\(\\sqrt{32}\\))<br \/>\n= \\(12\\sqrt{32}\\) \/ 32<br \/>\n= \\(3\\sqrt{32}\\) \/ 8<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{4}{\\sqrt{11}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{4}{\\sqrt{11}}\\)<br \/>\nTo rationalize the denominator, multiply and divide the given fraction with \\(\\sqrt{11}\\)<br \/>\n= \\(\\frac{4}{\\sqrt{11}}\\) \u00d7 (\\(\\sqrt{11}\\) \/ \\(\\sqrt{11}\\))<br \/>\n= \\(4\\sqrt{11}\\) \/ (\\(\\sqrt{11}\\) \u00d7 \\(\\sqrt{11}\\))<br \/>\n= \\(4\\sqrt{11}\\) \/ 11<\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt{\\frac{144}{13}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{\\frac{144}{13}}\\)<br \/>\nTo rationalize the denominator, multiply and divide the given fraction with \\(\\sqrt{13}\\)<br \/>\n\\(\\frac{\\sqrt{144}}{\\sqrt{13}}\\)<br \/>\n= \\(\\frac{\\sqrt{144}}{\\sqrt{13}}\\) \u00d7 (\\(\\sqrt{13}\\) \/ \\(\\sqrt{13}\\))<br \/>\n= \\(\\sqrt{144 \u00d7 13}\\) \/ (\\(\\sqrt{13}\\) \u00d7 \\(\\sqrt{13}\\))<br \/>\n= 12\\(\\sqrt{13}\\) \/ 13<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt[3]{\\frac{54 x^{4}}{343 y^{6}}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt[3]{\\frac{54 x^{4}}{343 y ^{6}}}\\)<br \/>\n= \\(\\frac{\\sqrt[3]{54 x^{4}}}{\\sqrt[3]{343 y^{6}}}\\)<br \/>\n= \\(\\frac{\\sqrt[3]{27 x^{3} \u00d7 2x}}{\\sqrt[3]{343 y^{6}}}\\)<br \/>\n= \\(\\frac{3x\\sqrt[3]{ 2x}}{7 y^{2}}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt{\\frac{4 x^{2}}{28 y^{4} z^{5}}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{\\frac{4 x^{2}}{28 y^{4} z^{5}}}\\)<br \/>\n= \\(\\frac{\\sqrt{4 x^{2}}}{\\sqrt{28 y^{4} z^{5}}}\\)<br \/>\n= \\(\\frac{x}{y^{2} z^{2}\\sqrt{7z}}\\)<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{6}{5+\\sqrt{3}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{6}{5 + \\sqrt{3}}\\)<br \/>\nTo rationalize the denominator, multiply and divide the given fraction with \\(5 &#8211; \\sqrt{3}\\)<br \/>\n= \\(\\frac{6}{5 + \\sqrt{3}}\\) \u00d7 (\\(5 &#8211; \\sqrt{3}\\) \/ \\(5 &#8211; \\sqrt{3}\\))<br \/>\n= 6\\((5 &#8211; \\sqrt{3})\\) \/ (\\(5 + \\sqrt{3}\\) \u00d7 \\(5 &#8211; \\sqrt{3}\\))<br \/>\n= 6\\((5 &#8211; \\sqrt{3})\\) \/ 22<br \/>\n= 6\\((5 &#8211; \\sqrt{3})\\) \/ 22<\/p>\n<p>Question 10.<br \/>\n2\\(\\sqrt{5}\\) + 7\\(\\sqrt{10}\\) &#8211; 3\\(\\sqrt{20}\\)<br \/>\nAnswer:<br \/>\n2\\(\\sqrt{5}\\) + 7\\(\\sqrt{10}\\) &#8211; 3\\(\\sqrt{20}\\)<br \/>\n= 2\\(\\sqrt{5}\\) + 7\\(\\sqrt{10}\\) &#8211; 3\\(\\sqrt{5 \u00d7 4}\\)<br \/>\n= 2\\(\\sqrt{5}\\) + 7\\(\\sqrt{10}\\) &#8211; 3 (2)\\(\\sqrt{5}\\)<br \/>\n= 2\\(\\sqrt{5}\\) + 7\\(\\sqrt{10}\\) &#8211; 6\\(\\sqrt{5}\\)<br \/>\n= \\(\\sqrt{5}\\) ( 2 &#8211; 6) + 7\\(\\sqrt{10}\\)<br \/>\n= \\(\\sqrt{5}\\) (-4) + 7\\(\\sqrt{10}\\)<br \/>\n= -4\\(\\sqrt{5}\\) + 7\\(\\sqrt{10}\\)<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{10}{\\sqrt{8}-\\sqrt{10}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{10}{\\sqrt{8}-\\sqrt{10}}\\)<br \/>\nTo rationalize the denominator, multiply and divide the given fraction with \\(\\sqrt{8} +\\sqrt{10} \\)<br \/>\n= \\(\\frac{10}{\\sqrt{8}-\\sqrt{10}}\\) \u00d7 (\\(\\sqrt{8} +\\sqrt{10} \\) \/ \\(\\sqrt{8} +\\sqrt{10} \\))<br \/>\n= 10(\\(\\sqrt{8} +\\sqrt{10} \\)) \/ (\\(\\sqrt{8} -\\sqrt{10} \\) \u00d7 \\(\\sqrt{8} +\\sqrt{10} \\))<br \/>\n= 10(\\(\\sqrt{8} +\\sqrt{10}\\)) \/ -2<br \/>\n= &#8211; 10(\\(\\sqrt{8} +\\sqrt{10} \\))\/ 2<\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt{6}\\)(7\\(\\sqrt{12}\\) &#8211; 4\\(\\sqrt{3}\\))<br \/>\nAnswer:<br \/>\n\\(\\sqrt{6}\\)(7\\(\\sqrt{12}\\) &#8211; 4\\(\\sqrt{3}\\))<br \/>\n= \\(\\sqrt{6}\\)(-4\\(\\sqrt{3}\\) + 7\\(\\sqrt{4 \u00d7 3}\\))<br \/>\n= \\(\\sqrt{6}\\)(-4\\(\\sqrt{3}\\) + 7 (2)\\(\\sqrt{3}\\))<br \/>\n= \\(\\sqrt{6}\\)(-4\\(\\sqrt{3}\\) + 14\\(\\sqrt{3}\\))<br \/>\n= \\(\\sqrt{6}\\)(\\(\\sqrt{3}\\) (14 &#8211; 4))<br \/>\n= \\(\\sqrt{6}\\)(\\(\\sqrt{3}\\) (12))<br \/>\n= 12(\\(\\sqrt{3}\\))(\\(\\sqrt{6}\\) )<br \/>\n= 12\\(\\sqrt{18}\\)<br \/>\n= 12\\(\\sqrt{9 \u00d7 2}\\)<br \/>\n= 36\\(\\sqrt{2}\\)<\/p>\n<p><strong>Use the graph to solve the equation.<\/strong><br \/>\nQuestion 13.<br \/>\nx<sup>2<\/sup> &#8211; 2x &#8211; 3 = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35326\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-q-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations q 1\" width=\"199\" height=\"195\" \/><br \/>\nAnswer:<br \/>\nThe solutions of the equations are the x-intercepts of those equations when we draw the graph for them<br \/>\nThe solutions of the given equation are -1 and 3<\/p>\n<p>Question 14.<br \/>\nx<sup>2<\/sup> &#8211; 2x + 3 = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35327\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-q-2.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations q 2\" width=\"185\" height=\"194\" \/><br \/>\nAnswer:<br \/>\nThe solutions of the equations are the x-intercepts of those equations when we draw the graph for them<br \/>\nThere are no real solutions for the given equation<\/p>\n<p>Question 15.<br \/>\nx<sup>2<\/sup> + 10x + 25 = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35328\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-q-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations q 3\" width=\"208\" height=\"198\" \/><br \/>\nAnswer:<br \/>\nThe solutions of the equations are the x-intercepts of those equations when we draw the graph for them<br \/>\nThe solution of the given equation is -5<\/p>\n<p><strong>Solve the equation by graphing.<\/strong><br \/>\nQuestion 16.<br \/>\nx<sup>2<\/sup> + 9x + 14 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114422\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-55.png\" alt=\"\" width=\"475\" height=\"507\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-55.png 475w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-55-281x300.png 281w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><br \/>\nThe solutions of the given equation are -2 and -7<\/p>\n<p>Question 17.<br \/>\nx<sup>2<\/sup> &#8211; 7x = 8<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114424\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-56.png\" alt=\"\" width=\"480\" height=\"498\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-56.png 480w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-56-289x300.png 289w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><br \/>\nThe solutions of the given equation are -1 and 8<\/p>\n<p>Question 18.<br \/>\nx + 4 = -x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114427\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-57.png\" alt=\"\" width=\"476\" height=\"502\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-57.png 476w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-57-284x300.png 284w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><\/p>\n<p>There are no real solutions for the given equation<\/p>\n<p><strong>Solve the equation using square roots.<\/strong><br \/>\nQuestion 19.<br \/>\n4x<sup>2<\/sup> = 64<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114429\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-58.png\" alt=\"\" width=\"307\" height=\"272\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-58.png 307w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-58-300x266.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p>\n<p>Question 20.<br \/>\n-3x<sup>2<\/sup> + 6 = 10<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114431\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-59.png\" alt=\"\" width=\"343\" height=\"411\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-59.png 343w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-59-250x300.png 250w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><br \/>\nThere are no real solutions for the given equation<\/p>\n<p>Question 21.<br \/>\n(x &#8211; 8)<sup>2<\/sup> = 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114433\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-60.png\" alt=\"\" width=\"426\" height=\"396\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-60.png 426w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-60-300x279.png 300w\" sizes=\"(max-width: 426px) 100vw, 426px\" \/><\/p>\n<p>Question 22.<br \/>\nExplain how to determine the number of real solutions of x<sup>2<\/sup> = 100 without solving.<br \/>\nAnswer:<br \/>\nx\u00b2 = 100<br \/>\nx\u00b2 &#8211; 100 = 0<br \/>\nx\u00b2 -a = 0<br \/>\nThe number of real solutions for the given equation is: 2<\/p>\n<p>Question 23.<br \/>\nThe length of a rectangular prism is four times its width. The volume of the prism is 380 cubic meters. Find the length and width of the prism.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35329\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-q-4.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations q 4\" width=\"264\" height=\"100\" \/><br \/>\nAnswer:<br \/>\nThe length of a rectangular prism is 4 times its width<br \/>\nThe height of the rectangular prism is: 5m<br \/>\nl = 4w<br \/>\nThe volume of the rectangular prism = l \u00d7 w \u00d7 h<br \/>\n380 = w \u00d7 4w \u00d7 5<br \/>\n4w\u00b2 = \\(\\frac{380}{5}\\)<br \/>\n4w\u00b2 = 76<br \/>\nw\u00b2 = \\(\\frac{76}{4}\\)<br \/>\nw\u00b2 = 19<br \/>\n\u221aw\u00b2 = \u221a19<br \/>\nw = \u221a19 or w = -\u221a19<br \/>\nThe width of the rectangular prism can&#8217;t be negative<br \/>\nw = \u221a19<br \/>\nl = 4\u221a19<\/p>\n<p>Question 24.<br \/>\nYou cast a fishing lure into the water from a height of 4 feet above the water. The height h (in feet) of the fishing lure after t seconds can be modeled by the equation h = -16t<sup>2<\/sup> + 24t + 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35330\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-q-5.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations q 5\" width=\"298\" height=\"189\" \/><br \/>\na. After how many seconds does the fishing lure reach a height of 12 feet?<br \/>\nAnswer:<br \/>\nh = -16t\u00b2 + 24t + 4<br \/>\n12 = -16t\u00b2 + 24t + 4<br \/>\n-16t\u00b2 + 24t = 12 &#8211; 4<br \/>\n-16t\u00b2 + 24t = 8<br \/>\n-2t\u00b2 + 3t = 1<br \/>\n2t\u00b2 &#8211; 3t + 1 = 0<br \/>\n2t\u00b2 &#8211; 2t &#8211; t + 1 = 0<br \/>\n2t (t &#8211; 1) &#8211; 1 (t &#8211; 1) = 0<br \/>\n(2t &#8211; 1) (t &#8211; 1) = 0<br \/>\n2t &#8211; 1 = 0 or t &#8211; 1 = 0<br \/>\n2t = 1 or t = 1<br \/>\nt = \\(\\frac{1}{2}\\) or t = 1<\/p>\n<p>b. After how many seconds does the fishing lure hit the water?<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe values of t are: [laex]\\frac{1}{2}[\/latex] and 1<br \/>\nSo,<br \/>\nAfter 1 second, the fishing lure will hit the water<\/p>\n<h3><a id=\"Lesson_9.4_Solving_Quadratic_Equations_by_Completing_the_Square\"><\/a>Lesson 9.4 Solving Quadratic Equations by Completing the Square<\/h3>\n<p><strong>Essential Question<\/strong> How can you use \u201ccompleting the square\u201d to solve a quadratic equation?<br \/>\nAnswer:<br \/>\nThe steps to &#8220;Completing the Square&#8221; to solve a quadratic equation are:<br \/>\n1. Divide all terms by a (The coefficient of x\u00b2)<br \/>\n2. Move the number term (c \/ a) to the right side of the equation<br \/>\n3. Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Solving by Completing the Square<br \/>\nWork with a partner.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35331\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 1\" width=\"294\" height=\"453\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-1.png 294w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-1-195x300.png 195w\" sizes=\"(max-width: 294px) 100vw, 294px\" \/><br \/>\na. Write the equation modeled by the algebra tiles. This is the equation to be solved.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114703\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-61.png\" alt=\"\" width=\"255\" height=\"147\" \/><br \/>\nx\u00b2 + 4x = -2<\/p>\n<p>b. Four algebra tiles are added to the left side to \u201ccomplete the square.\u201d Why are four algebra tiles also added to the right side?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114705\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-62.png\" alt=\"\" width=\"265\" height=\"149\" \/><br \/>\nThe four algebra tiles are added to the right side for the purpose of &#8220;Completing the square&#8221;<br \/>\nThe same four algebra tiles also have to be added to the right side to balance the equation<br \/>\nWe added four algebra tiles to the right side also<\/p>\n<p>c. Use algebra tiles to label the dimensions of the square on the left side and simplify on the right side.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114705\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-62.png\" alt=\"\" width=\"265\" height=\"149\" \/><br \/>\nBlue tile (Represents the coefficient of x\u00b2)<br \/>\nGreen tile (Represents the coefficient of x)<br \/>\nYellow and Red tiles (represent the constant terms)<\/p>\n<p>d. Write the equation modeled by the algebra tiles so that the left side is the square of a binomial. Solve the equation using square roots.<br \/>\nAnswer:<br \/>\nx\u00b2 + 4x = -2<br \/>\nx\u00b2 + 4x + 4 = -2 + 4<br \/>\n(x + 2)\u00b2 = 2<br \/>\n\u221a(x + 2)\u00b2 = \u221a2<br \/>\nx + 2 = \u221a2 or x + 2 = -\u221a2<br \/>\nx = \u221a2 &#8211; 2 or x = -(\u221a2 + 2)<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Solving by Completing the Square<br \/>\nWork with a partner.<br \/>\na. Write the equation modeled by the algebra tiles.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35332\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 2\" width=\"501\" height=\"291\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-2.png 501w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-2-300x174.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><br \/>\nAnswer:<br \/>\nFrom the given algebra tiles representation,<br \/>\nThe equation that can be modeled is x\u00b2 + 6x = -5<\/p>\n<p>b. Use algebra tiles to \u201ccomplete the square.\u201d<br \/>\nAnswer:<br \/>\nThe equation modeled by algebra tiles is x\u00b2 + 6x = -5<br \/>\nTo solve the quadratic equation by using algebra tiles,<br \/>\nx\u00b2 + 6x + 9 = -5 + 9<br \/>\n(x + 3)\u00b2 = 4<\/p>\n<p>c. Write the solutions of the equation.<br \/>\nAnswer:<br \/>\n(x + 3)\u00b2 = 4<br \/>\n\u221a(x + 3)\u00b2 = \u221a4<br \/>\nx + 3 = 2 or x + 3 = -2<br \/>\nx = 2 &#8211; 3 or x = -2 &#8211; 3<br \/>\nx = -1 or x = -5<\/p>\n<p>d. Check each solution in the original equation.<br \/>\nAnswer:<br \/>\n(x + 3)\u00b2 = 4<br \/>\nPut x = -1 and -5 in the above equation<br \/>\nFor x = -1,<br \/>\n(-1 + 3)\u00b2 = 4<br \/>\n(2)\u00b2 = 4<br \/>\n4 = 4<br \/>\nFor x = -5,<br \/>\n(-5 + 3)\u00b2 = 4<br \/>\n(-2)\u00b2 = 4<br \/>\n4 = 4<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you use \u201ccompleting the square\u201d to solve a quadratic equation?<br \/>\nAnswer:<br \/>\nThe steps to &#8220;Completing the Square&#8221; to solve a quadratic equation are:<br \/>\n1. Divide all terms by a (The coefficient of x\u00b2)<br \/>\n2. Move the number term (c \/ a) to the right side of the equation<br \/>\n3. Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation<\/p>\n<p>Question 4.<br \/>\nSolve each quadratic equation by completing the square.<br \/>\na. x<sup>2<\/sup> &#8211; 2x = 1<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 2x = 1<br \/>\nx\u00b2 &#8211; 2x &#8211; 1 = 0<br \/>\nx\u00b2 &#8211; 2x = 1<br \/>\nx\u00b2 &#8211; 2x + 1 = 1 + 1<br \/>\n(x &#8211; 1)\u00b2 = 2<\/p>\n<p>b. x<sup>2<\/sup> &#8211; 4x = -1<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 4x = -1<br \/>\nx\u00b2 &#8211; 4x + 1 = 0<br \/>\nx\u00b2 &#8211; 4x = -1<br \/>\nx\u00b2 &#8211; 4x + 4 = -1 + 4<br \/>\n(x &#8211; 2)\u00b2 = 3<\/p>\n<p>c. x<sup>2<\/sup> + 4x = -3<br \/>\nAnswer:<br \/>\nx\u00b2 + 4x = -3<br \/>\nx\u00b2 + 4x + 3 = 0<br \/>\nx\u00b2 + 4x = -3<br \/>\nx\u00b2 + 4x + 4 = -3 + 4<br \/>\n(x + 2)\u00b2 = 1<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Complete the square for the expression. Then factor the trinomial.<\/strong><br \/>\nQuestion 1.<br \/>\nx<sup>2<\/sup> + 10x<br \/>\nAnswer:<br \/>\nx\u00b2 + 10x<br \/>\nax\u00b2 + bx<br \/>\na = 1 and b = 10<br \/>\n\\(\\frac{b}{2}\\) = \\(\\frac{10}{2}\\)<br \/>\n\\(\\frac{b}{2}\\) = 5<br \/>\n\\(\\frac{b\u00b2}{4}\\) = 5\u00b2 = 25<br \/>\nx\u00b2 + 10x + 25 = (x + 5)\u00b2<\/p>\n<p>Question 2.<br \/>\nx<sup>2<\/sup> &#8211; 4x<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 4x<br \/>\nax\u00b2 + bx<br \/>\na = 1 and b = -4<br \/>\n\\(\\frac{b}{2}\\) = \\(\\frac{-4}{2}\\)<br \/>\n\\(\\frac{b}{2}\\) = -2<br \/>\n\\(\\frac{b\u00b2}{4}\\) = (-2)\u00b2 = 4<br \/>\nx\u00b2 &#8211; 4x + 4 = (x &#8211; 2)\u00b2<\/p>\n<p>Question 3.<br \/>\nx<sup>2<\/sup> + 7x<br \/>\nAnswer:<br \/>\nx\u00b2 + 7x<br \/>\nax\u00b2 + bx<br \/>\na = 1 and b = 7<br \/>\n\\(\\frac{b}{2}\\) = \\(\\frac{7}{2}\\)<br \/>\n\\(\\frac{b\u00b2}{4}\\)<br \/>\n= \\(\\frac{49}{4}\\)<br \/>\nx\u00b2 + 7x + \\(\\frac{49}{4}\\) = (x + \\(\\frac{7}{2}\\))\u00b2<\/p>\n<p><strong>Solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.<\/strong><br \/>\nQuestion 4.<br \/>\nx<sup>2<\/sup> &#8211; 2x = 3<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 2x = 3<br \/>\nx\u00b2 + bx = d<br \/>\nb = -2 and d = 3<br \/>\n\\(\\frac{b\u00b2}{4}\\) = \\(\\frac{4}{4}\\) = 1<br \/>\nx\u00b2 &#8211; 2x + 1 = 3 + 1<br \/>\n(x &#8211; 1)\u00b2 = 4<br \/>\n\u221a(x &#8211; 1)\u00b2 = \u221a4<br \/>\nx &#8211; 1 = 2 or x &#8211; 1 = -2<br \/>\nx = 2 + 1 or x = -2 + 1<br \/>\nx = 3 or x = -1<\/p>\n<p>Question 5.<br \/>\nm<sup>2<\/sup> + 12m = -8<br \/>\nAnswer:<br \/>\nm\u00b2 + 12m = -8<br \/>\nx\u00b2 + bx = d<br \/>\nb = 12 and d = -8<br \/>\n\\(\\frac{b\u00b2}{4}\\) = \\(\\frac{144}{4}\\) = 36<br \/>\nm\u00b2 + 12m + 36 = -8 + 36<br \/>\n(m + 6)\u00b2 = 28<br \/>\n\u221a(m + 6)\u00b2 = \u221a28<br \/>\nm + 6 = \u221a28 or m + 6 = -\u221a28<br \/>\nm = \u221a28 &#8211; 6 or m = -(\u221a28 + 6)<\/p>\n<p>Question 6.<br \/>\n3g<sup>2<\/sup> &#8211; 24g + 27 = 0<br \/>\nAnswer:<br \/>\n3g\u00b2 &#8211; 24g + 27 = 0<br \/>\n3(g\u00b2 &#8211; 8g + 9) = 0<br \/>\ng\u00b2 &#8211; 8g + 9 = 0<br \/>\ng\u00b2 &#8211; 8g = -9<br \/>\nx\u00b2 + bx = d<br \/>\nb = -8 and d = -9<br \/>\n\\(\\frac{b\u00b2}{4}\\) = \\(\\frac{64}{4}\\) = 16<br \/>\ng\u00b2 &#8211; 8g + 16 = -9 + 16<br \/>\n(g &#8211; 4)\u00b2 = 7<br \/>\n\u221a(g &#8211; 4)\u00b2 = \u221a7<br \/>\ng &#8211; 4 = \u221a7 or g &#8211; 4 = -\u221a7<br \/>\ng = \u221a7 + 4 or g = -\u221a7 + 4<\/p>\n<p><strong>Determine whether the quadratic function has a maximum or minimum value. Then find the value.<\/strong><br \/>\nQuestion 7.<br \/>\ny = -x<sup>2<\/sup> &#8211; 4x + 4<br \/>\nAnswer:<br \/>\ny = -x\u00b2 &#8211; 4x + 4<br \/>\ny &#8211; 4 = -x\u00b2\u00a0 &#8211; 4x + 4 &#8211; 4<br \/>\ny &#8211; 4 = -x\u00b2\u00a0 &#8211; 4x<br \/>\ny &#8211; 4 = &#8211; (x\u00b2 + 4x)<br \/>\ny &#8211; 4 &#8211; 4 = -(x\u00b2 + 4x + 4)<br \/>\ny\u00a0 &#8211; 4= -(x + 2)\u00b2<br \/>\ny = -(x + 2)\u00b2 + 4<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114727\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-63.png\" alt=\"\" width=\"505\" height=\"498\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-63.png 505w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-63-300x296.png 300w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><br \/>\nThe given equation will have a minimum value<br \/>\nThe minimum value of the given equation is -4<\/p>\n<p>Question 8.<br \/>\ny = x<sup>2<\/sup> + 12x + 40<br \/>\nAnswer:<br \/>\ny = x\u00b2 + 12x + 40<br \/>\ny &#8211; 40 = x\u00b2\u00a0 + 12x + 40 &#8211; 40<br \/>\ny &#8211; 40 = x\u00b2\u00a0 + 12x<br \/>\ny &#8211; 40 + 36 = x\u00b2 + 12x + 36<br \/>\ny\u00a0 &#8211; 4= (x + 6)\u00b2<br \/>\ny = (x + 6)\u00b2 + 4<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114772\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-65.png\" alt=\"\" width=\"479\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-65.png 479w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-65-285x300.png 285w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nWe can observe that the graph is in an open shape<br \/>\nThe given equation will have a maximum value<br \/>\nThe maximum value of the given equation is 4<\/p>\n<p>Question 9.<br \/>\ny = x<sup>2<\/sup> &#8211; 2x &#8211; 2<br \/>\nAnswer:<br \/>\ny = x\u00b2 &#8211; 2x &#8211; 2<br \/>\ny + 2 = x\u00b2\u00a0 &#8211; 2x &#8211; 2 + 2<br \/>\ny + 2 = x\u00b2\u00a0 &#8211; 2x<br \/>\ny + 2 + 1 = x\u00b2 &#8211; 2x + 1<br \/>\ny\u00a0 + 3= (x &#8211; 1)\u00b2<br \/>\ny = (x &#8211; 1)\u00b2 &#8211; 3<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114775\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-66.png\" alt=\"\" width=\"474\" height=\"505\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-66.png 474w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-66-282x300.png 282w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><br \/>\nWe can observe that the graph is in an open shape<br \/>\nThe given equation will have a maximum value<br \/>\nThe maximum value of the given equation is 3<\/p>\n<p><strong>Determine whether the function could be represented by the graph in Example 6. Explain.<\/strong><br \/>\nQuestion 10.<br \/>\nh(x) = (x &#8211; 8)<sup>2<\/sup> + 10<br \/>\nAnswer:<br \/>\nh (x) = (x &#8211; 8)\u00b2 + 10<br \/>\nThe vertex point that is the solution for the given equation is (8, 10)<br \/>\nSince the values of x and y are positive, the graph must be in the 1st quadrant<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114779\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-67.png\" alt=\"\" width=\"479\" height=\"500\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-67.png 479w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-67-287x300.png 287w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nQuestion 11.<br \/>\nn(x) = -2(x &#8211; 5)(x &#8211; 20)<br \/>\nAnswer:<br \/>\nn (x) = -2 (x &#8211; 5) (x &#8211; 20)<br \/>\nThe vertex point that is the solution for the given equation is (-5, -20)<br \/>\nSince the values of x and y are positive, the graph must be in the 3rd quadrant<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114780\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-68.png\" alt=\"\" width=\"482\" height=\"497\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-68.png 482w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-68-291x300.png 291w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><\/p>\n<p>Question 12.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nRepeat Example 7 when the function is y = -16x<sup>2<\/sup> + 128x.<br \/>\nAnswer:<br \/>\ny = -16x\u00b2 + 128x<br \/>\ny = -16(x\u00b2 &#8211; 8x)<br \/>\ny &#8211; 16 = -16(x\u00b2 &#8211; 8x + 16)<br \/>\ny &#8211; 16 = -16(x &#8211; 4)\u00b2<br \/>\ny = -16 (x &#8211; 4)\u00b2 + 16<br \/>\na) The maximum height of the rocket:<br \/>\nWe can observe that the maximum value is 16<br \/>\nWe can conclude that the model rocket reaches a maximum height of 16 feet<br \/>\nb) The axes of symmetry:<br \/>\nFrom the given equation that we obtained in the vertex form,<br \/>\nThe vertex is (4, 16)<br \/>\nThe axis of symmetry is x = 4<\/p>\n<p>Question 13.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nYou want the chalkboard to cover 4 square feet. Find the width of the border to the nearest inch.<br \/>\nAnswer:<br \/>\nFrom Example 8,<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114783\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-69.png\" alt=\"\" width=\"201\" height=\"195\" \/><br \/>\nThe length of the chalkboard = 7 &#8211; 2x<br \/>\nThe width of the chalkboard = 3 &#8211; 2x<br \/>\nArea of the rectangle = Length \u00d7 Width<br \/>\n4 = (7 &#8211; 2x) (3 &#8211; 2x)<br \/>\n21 &#8211; 14x &#8211; 6x + 4x\u00b2 = 4<br \/>\n4x\u00b2 &#8211; 20x + 21 = 4<br \/>\n4x\u00b2 &#8211; 20x = 4 &#8211; 21<br \/>\n4x\u00b2 &#8211; 20x = -17<br \/>\n4 (x\u00b2 &#8211; 5x) = -17<br \/>\nx\u00b2 &#8211; 5x = &#8211;\\(\\frac{17}{4}\\)<br \/>\nx\u00b2 &#8211; 5x + \\(\\frac{25}{4}\\) = &#8211;\\(\\frac{17}{4}\\) + \\(\\frac{25}{4}\\)<br \/>\nx\u00b2 &#8211; 5x + \\(\\frac{25}{4}\\) = 2<br \/>\n(x &#8211; \\(\\frac{5}{2}\\))\u00b2 = 2<br \/>\n\u221a(x &#8211; \\(\\frac{5}{2}\\))\u00b2 = \u221a2<br \/>\nx &#8211; \\(\\frac{5}{2}\\) = \u221a2 or x &#8211; \\(\\frac{5}{2}\\) = -\u221a2<br \/>\nx = 1.414 + 2.5 or x = -1.414 + 2.5<br \/>\nx = 3.91 or x = 1.08<br \/>\nThe width of the border = 1.08 foot<br \/>\n1.08 \u00d7 12 inches = 12.96 inches<br \/>\nThe width of the border in inches is 12.96 inches<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_by_Completing_the_Square_9.4_Exercises\"><\/a>Solving Quadratic Equations by Completing the Square 9.4 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe process of adding a constant c to the expression x<sup>2<\/sup> + bx so that x<sup>2<\/sup> + bx + c is a perfect square trinomial is called ________________.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42062\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 1\" width=\"540\" height=\"86\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-1.png 540w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-1-300x48.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nExplain how to complete the square for an expression of the form x<sup>2<\/sup> + bx.<br \/>\nAnswer:<br \/>\nThe steps that are required to complete the square for an expression x\u00b2 + bx are:<br \/>\n1. Find one half of b i.e., \\(\\frac{b}{2}\\)<br \/>\n2. Find \\(\\frac{b\u00b2}{4}\\) and add it to the expression x\u00b2 + bx<br \/>\nx\u00b2 + bx + \\(\\frac{b\u00b2}{4}\\)<\/p>\n<p>Question 3.<br \/>\n<strong>WRITING<\/strong><br \/>\nIs it more convenient to complete the square for x<sup>2<\/sup> + bx when b is odd or when b is even? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42063\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-3.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 3\" width=\"546\" height=\"87\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-3.png 546w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-3-300x48.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe how you can use the process of completing the square to find the maximum or minimum value of a quadratic function.<br \/>\nAnswer:<br \/>\nThere are two ways to find the absolute maximum\/minimum value for f(x) = ax\u00b2 + bx + c<br \/>\nf(x) = a(x \u2212 h)\u00b2 + k, and the absolute maximum\/minimum value\u00a0is k and it occurs at x = h.<br \/>\nIf a &gt; 0, then the parabola opens up, and it is a minimum functional value of f (x)<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u201310, find the value of c that completes the square.<\/strong><br \/>\nQuestion 5.<br \/>\nx<sup>2<\/sup> &#8211; 8x + c<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42064\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-5.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 5\" width=\"257\" height=\"87\" \/><\/p>\n<p>Question 6.<br \/>\nx<sup>2<\/sup> &#8211; 2x + c<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 2x + c<br \/>\nx\u00b2 + bx + c<br \/>\nb = -2<br \/>\nx\u00b2 + bx + \\(\\frac{b\u00b2}{4}\\)<br \/>\nc = \\(\\frac{b\u00b2}{4}\\)<br \/>\nc = \\(\\frac{4}{4}\\)<br \/>\nc = 1<\/p>\n<p>Question 7.<br \/>\nx<sup>2<\/sup> + 4x + c<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42065\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-7.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 7\" width=\"186\" height=\"87\" \/><\/p>\n<p>Question 8.<br \/>\nx<sup>2<\/sup> + 12x + c<br \/>\nAnswer:<br \/>\nx\u00b2 + 12x + c<br \/>\nx\u00b2 + bx + c<br \/>\nb = 12<br \/>\nx\u00b2 + bx + \\(\\frac{b\u00b2}{4}\\)<br \/>\nc = \\(\\frac{b\u00b2}{4}\\)<br \/>\nc = \\(\\frac{144}{4}\\)<br \/>\nc = 36<\/p>\n<p>Question 9.<br \/>\nx<sup>2<\/sup> &#8211; 15x + c<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42066\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-9.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 9\" width=\"182\" height=\"87\" \/><\/p>\n<p>Question 10.<br \/>\nx<sup>2<\/sup> + 9x + c<br \/>\nAnswer:<br \/>\nx\u00b2 + 9x + c<br \/>\nx\u00b2 + bx + c<br \/>\nb = 9<br \/>\nx\u00b2 + bx + \\(\\frac{b\u00b2}{4}\\)<br \/>\nc = \\(\\frac{b\u00b2}{4}\\)<br \/>\nc = \\(\\frac{81}{4}\\)<\/p>\n<p><strong>In Exercises 11\u201316, complete the square for the expression. Then factor the trinomial.<\/strong><br \/>\nQuestion 11.<br \/>\nx<sup>2<\/sup> &#8211; 10x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42067\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-11.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 11\" width=\"307\" height=\"190\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-11.png 307w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-11-300x186.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p>\n<p>Question 12.<br \/>\nx<sup>2<\/sup> &#8211; 40x<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 40x<br \/>\nax\u00b2 + bx<br \/>\na = 1 and b = -40<br \/>\n\\(\\frac{b}{2}\\) = \\(\\frac{-40}{2}\\)<br \/>\n\\(\\frac{b}{2}\\) = -20<br \/>\n\\(\\frac{b\u00b2}{4}\\) = (-20)\u00b2 = 400<br \/>\nx\u00b2 &#8211; 40x + 200 = (x &#8211; 20)\u00b2<\/p>\n<p>Question 13.<br \/>\nx<sup>2<\/sup> + 16x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42068\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-13.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 13\" width=\"293\" height=\"194\" \/><\/p>\n<p>Question 14.<br \/>\nx<sup>2<\/sup> + 22x<br \/>\nAnswer:<br \/>\nx\u00b2 + 22x<br \/>\nax\u00b2 + bx<br \/>\na = 1 and b = 22<br \/>\n\\(\\frac{b}{2}\\) = \\(\\frac{22}{2}\\)<br \/>\n\\(\\frac{b}{2}\\) = 11<br \/>\n\\(\\frac{b\u00b2}{4}\\) = 11\u00b2 = 121<br \/>\nx\u00b2 + 22x + 121 = (x + 11)\u00b2<\/p>\n<p>Question 15.<br \/>\nx<sup>2<\/sup> + 5x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42069\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-15.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 15\" width=\"304\" height=\"265\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-15.png 304w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-15-300x262.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/p>\n<p>Question 16.<br \/>\nx<sup>2<\/sup> &#8211; 3x<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 3x<br \/>\nax\u00b2 + bx<br \/>\na = 1 and b = -3<br \/>\n\\(\\frac{b}{2}\\) = \\(\\frac{-3}{2}\\)<br \/>\n\\(\\frac{b}{2}\\) = &#8211;\\(\\frac{3}{2}\\)<br \/>\n\\(\\frac{b\u00b2}{4}\\) = \\(\\frac{9}{4}\\)<br \/>\nx\u00b2 &#8211; 3x + \\(\\frac{9}{4}\\) = (x &#8211; \\(\\frac{3}{2}\\))\u00b2<\/p>\n<p><strong>In Exercises 17\u201322, solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.<\/strong><br \/>\nQuestion 17.<br \/>\nx<sup>2<\/sup> + 14x = 15<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42070\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-17.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 17\" width=\"555\" height=\"307\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-17.png 555w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-17-300x166.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 18.<br \/>\nx<sup>2<\/sup> &#8211; 6x = 16<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 6x = 16<br \/>\nx\u00b2 &#8211; 6x + 9 = 16 + 9<br \/>\n(x &#8211; 3)\u00b2 = 25<br \/>\n\u221a(x &#8211; 3)\u00b2 = \u221a25<br \/>\nx &#8211; 3 = 5 or x &#8211; 3 = -5<br \/>\nx = 5 + 3 or x = -5 + 3<br \/>\nx = 8 or x = -2<\/p>\n<p>Question 19.<br \/>\nx<sup>2<\/sup> &#8211; 4x = -2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42071\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-19.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 19\" width=\"402\" height=\"335\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-19.png 402w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-19-300x250.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<p>Question 20.<br \/>\nx<sup>2<\/sup> + 2x = 5<br \/>\nAnswer:<br \/>\nx\u00b2 + 2x = 5<br \/>\nx\u00b2 + 2x + 1 = 5 + 1<br \/>\n(x + 1)\u00b2 = 6<br \/>\n\u221a(x + 1)\u00b2 = \u221a6<br \/>\nx + 1 = \u221a6 or x + 1 = -\u221a6<br \/>\nWe know that,<br \/>\n\u221a6 = 2.44<br \/>\nx = 2.44 &#8211; 1 or x = -2.44 &#8211; 1<br \/>\nx = 1.44 or x = -3.44<\/p>\n<p>Question 21.<br \/>\nx<sup>2<\/sup> &#8211; 5x = 8<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42072\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-21.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 21\" width=\"402\" height=\"608\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-21.png 402w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-21-198x300.png 198w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<p>Question 22.<br \/>\nx<sup>2<\/sup> + 11x = -10<br \/>\nAnswer:<br \/>\nx\u00b2 + 11x = -10<br \/>\nx\u00b2 + 11x + \\(\\frac{121}{4}\\) = -10 + \\(\\frac{121}{4}\\)<br \/>\n(x + 11)\u00b2 = \\(\\frac{81}{4}\\)<br \/>\n\u221a(x + 11)\u00b2 = \u221a\\(\\frac{81}{4}\\)<br \/>\nx + 11 = \u221a\\(\\frac{81}{4}\\) or x + 11 = -\u221a\\(\\frac{81}{4}\\)<br \/>\nx = 20.25 &#8211; 11 or x = -20.25 &#8211; 11<br \/>\nx = 9.25 or x = -31.25<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe area of the patio is 216 square feet.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35333\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-3.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 3\" width=\"151\" height=\"135\" \/><br \/>\na. Write an equation that represents the area of the patio.<br \/>\nb. Find the dimensions of the patio by completing the square.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42073\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-23.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 23\" width=\"547\" height=\"689\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-23.png 547w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-23-238x300.png 238w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nSome sand art contains sand and water sealed in a glass case, similar to the one shown. When the art is turned upside down, the sand, and waterfall to create a new picture. The glass case has a depth of 1 centimeter and a volume of 768 cubic centimeters.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35334\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-4.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 4\" width=\"280\" height=\"135\" \/><br \/>\na. Write an equation that represents the volume of the glass case.<br \/>\nAnswer:<br \/>\nThe volume of the glass case = L \u00d7 W \u00d7 H<br \/>\n768 = x (x &#8211; 8) \u00d7 1<br \/>\nx\u00b2 &#8211; 8x = 768<\/p>\n<p>b. Find the dimensions of the glass case by completing the square.<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 8x = 768<br \/>\nx\u00b2 &#8211; 8x + 16 = 768 + 16<br \/>\n(x &#8211; 4)\u00b2 = 784<br \/>\n\u221a(x &#8211; 4)\u00b2 = \u221a784<br \/>\nx &#8211; 4 = 28 or x &#8211; 4 = -28<br \/>\nx = 28 + 4 or x = -28 + 4<br \/>\nx = 32 or x = -24<br \/>\nx = 32<br \/>\nLength of the glass case = x &#8211; 8 = 32 &#8211; 8 =24 cm<br \/>\nWidth of the glass case = x = 32 cm<\/p>\n<p><strong>In Exercises 25\u201332, solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.<\/strong><br \/>\nQuestion 25.<br \/>\nx<sup>2<\/sup> &#8211; 8x + 15 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42074\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-25.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 25\" width=\"506\" height=\"379\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-25.png 506w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-25-300x225.png 300w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><\/p>\n<p>Question 26.<br \/>\nx<sup>2<\/sup> + 4x &#8211; 21 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 + 4x &#8211; 21 = 0<br \/>\nx\u00b2 + 4x &#8211; 21 + 21 = 0 + 21<br \/>\nx\u00b2 + 4x = 21<br \/>\nx\u00b2 + 4x + 4 = 21 + 4<br \/>\n(x + 2)\u00b2 = 25<br \/>\n\u221a(x + 2)\u00b2 = \u221a25<br \/>\nx + 2 = 5 or x + 2 = -5<br \/>\nx = 5 &#8211; 2 or x = -5 &#8211; 2<br \/>\nx = 3 or x = -7<\/p>\n<p>Question 27.<br \/>\n2x<sup>2<\/sup> + 20x + 44 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42075\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-27.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 27\" width=\"435\" height=\"497\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-27.png 435w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-27-263x300.png 263w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><\/p>\n<p>Question 28.<br \/>\n3x<sup>2<\/sup> &#8211; 18x + 12 = 0<br \/>\nAnswer:<br \/>\n3x\u00b2 &#8211; 18x + 12 = 0<br \/>\n3 (x\u00b2 &#8211; 6x + 4) = 0<br \/>\nx\u00b2 &#8211; 6x + 4 = 0<br \/>\nx\u00b2 &#8211; 6x &#8211; 4 + 4 = 0 + 4<br \/>\nx\u00b2 &#8211; 6x = 4<br \/>\nx\u00b2 &#8211; 6x + 9 = 9 + 4<br \/>\n(x &#8211; 3)\u00b2 = 13<br \/>\n\u221a(x &#8211; 3)\u00b2 = \u221a13<br \/>\nx &#8211; 3 = 3.60 or x &#8211; 3 = -3.60<br \/>\nx = 3.60 + 3 or x = -3.60 + 3<br \/>\nx = 6.60 or x = -0.60<\/p>\n<p>Question 29.<br \/>\n-3x<sup>2<\/sup> &#8211; 24x + 17 = -40<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42076\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-29.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 29\" width=\"422\" height=\"497\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-29.png 422w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-29-255x300.png 255w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><\/p>\n<p>Question 30.<br \/>\n-5x<sup>2<\/sup> &#8211; 20x + 35 = 30<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114806\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-70.png\" alt=\"\" width=\"771\" height=\"794\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-70.png 771w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-70-291x300.png 291w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-70-768x791.png 768w\" sizes=\"(max-width: 771px) 100vw, 771px\" \/><\/p>\n<p>Question 31.<br \/>\n2x<sup>2<\/sup> &#8211; 14x + 10 = 26<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42077\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-31.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 31\" width=\"418\" height=\"744\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-31.png 418w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-31-169x300.png 169w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<p>Question 32.<br \/>\n4x<sup>2<\/sup> + 12x &#8211; 15 = 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-114808\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-71.png\" alt=\"\" width=\"761\" height=\"993\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-71.png 761w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-71-230x300.png 230w\" sizes=\"(max-width: 761px) 100vw, 761px\" \/><\/p>\n<p>Question 33.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving x<sup>2<\/sup> + 8x = 10 by completing the square.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35335\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-5.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 5\" width=\"316\" height=\"127\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-5.png 316w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-5-300x121.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42078\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-33.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 33\" width=\"516\" height=\"399\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-33.png 516w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-33-300x232.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in the first two steps of solving 2x<sup>2<\/sup> &#8211; 2x &#8211; 4 = 0 by completing the square.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35336\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-6.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 6\" width=\"271\" height=\"97\" \/><br \/>\nAnswer:<br \/>\n2x\u00b2 &#8211; 2x &#8211; 4 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\nx\u00b2 &#8211; x &#8211; 2 = 0<br \/>\nx\u00b2 &#8211; x = 2<br \/>\nx\u00b2 &#8211; x + \\(\\frac{1}{4}\\) = 2+ \\(\\frac{1}{4}\\)<br \/>\n(x &#8211; \\(\\frac{1}{2}\\))\u00b2 = \\(\\frac{9}{4}\\)<\/p>\n<p>Question 35.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nFind all values of b for which x<sup>2<\/sup> + bx + 25 is a perfect square trinomial. Explain how you found your answer.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42079\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-35.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 35\" width=\"545\" height=\"444\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-35.png 545w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-35-300x244.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou are completing the square to solve 3x<sup>2<\/sup> + 6x = 12. What is the first step?<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n3x\u00b2 + 6x = 12<br \/>\n3(x\u00b2 + 2x) = 3(4)<br \/>\nx\u00b2 + 2x = 4<\/p>\n<p><strong>In Exercises 37\u201340, write the function in vertex form by\ue04acompleting the square. Then match the function with its graph.<\/strong><br \/>\nQuestion 37.<br \/>\ny = x<sup>2<\/sup> + 6x + 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42080\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-37.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 37\" width=\"572\" height=\"340\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-37.png 572w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-37-300x178.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 38.<br \/>\ny = -x<sup>2<\/sup> + 8x &#8211; 12<br \/>\nAnswer:<br \/>\ny = -x\u00b2 + 8x &#8211; 12<br \/>\ny + 12 = -x\u00b2 + 8x &#8211; 12+ 12<br \/>\ny + 12 = -x\u00b2 + 8x<br \/>\ny + 12 = &#8211; (x\u00b2 &#8211; 8x)<br \/>\ny + 12 &#8211; 16 = &#8211; (x\u00b2 &#8211; 8x + 16)<br \/>\ny &#8211; 4 = &#8211; (x &#8211; 4)\u00b2<br \/>\ny = -(x &#8211; 4)\u00b2 + 4<br \/>\nThe vertex point is (-4, 4)<br \/>\nThe vertex point matches with graph A<\/p>\n<p>Question 39.<br \/>\ny = -x<sup>2<\/sup> &#8211; 4x &#8211; 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42081\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-39.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 39\" width=\"556\" height=\"376\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-39.png 556w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-39-300x203.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 40.<br \/>\ny = x<sup>2<\/sup> &#8211; 2x + 4<br \/>\nAnswer:<br \/>\ny = x\u00b2 &#8211; 2x + 4<br \/>\ny &#8211; 4 = x\u00b2 &#8211; 2x + 4 &#8211; 4<br \/>\ny &#8211; 4 = x\u00b2 &#8211; 2x<br \/>\ny &#8211; 4 + 1 = x\u00b2 &#8211; 2x + 1<br \/>\ny &#8211; 3 = (x &#8211; 1)\u00b2<br \/>\ny = (x &#8211; 1)\u00b2 + 3<br \/>\nThe vertex point is (1, 3)<br \/>\nThe vertex point matches with graph C<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35337\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-7.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 7\" width=\"333\" height=\"268\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-7.png 333w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-7-300x241.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/p>\n<p><strong>In Exercises 41\u201346, determine whether the quadratic function has a maximum or minimum value. Then find the value.<\/strong><br \/>\nQuestion 41.<br \/>\ny = x<sup>2<\/sup> &#8211; 4x &#8211; 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42082\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-41.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 41\" width=\"565\" height=\"361\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-41.png 565w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-41-300x192.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 42.<br \/>\ny = x<sup>2<\/sup> + 6x + 10<br \/>\nAnswer:<br \/>\ny = x\u00b2 + 6x + 10<br \/>\ny &#8211; 10 = x\u00b2 + 6x + 10 &#8211; 10<br \/>\ny &#8211; 10 = x\u00b2 + 6x<br \/>\ny &#8211; 10 + 9 = x\u00b2 + 6x + 9<br \/>\ny &#8211; 1 = (x + 3)\u00b2<br \/>\ny = (x + 3)\u00b2 + 1<br \/>\nThe vertex point is: (-3, 1)<br \/>\nFrom the above vertex point, the x-coordinate is negative<br \/>\nThe parabola closes down and the y-coordinate will be the maximum value of the given equation.<br \/>\nThe given equation has a maximum value and the maximum value of the given equation is: 1<\/p>\n<p>Question 43.<br \/>\ny = -x<sup>2<\/sup> &#8211; 10x &#8211; 30<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42083\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-43.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 43\" width=\"586\" height=\"400\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-43.png 586w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-43-300x205.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 44.<br \/>\ny = -x<sup>2<\/sup> + 14x &#8211; 34<br \/>\nAnswer:<br \/>\ny = -x\u00b2 + 14x &#8211; 34<br \/>\ny + 34 = -x\u00b2 + 14x + 34 &#8211; 34<br \/>\ny + 34 = -x\u00b2 + 14x<br \/>\ny + 34 = &#8211; (x\u00b2 &#8211; 14x)<br \/>\ny + 34 &#8211; 49 = &#8211; (x\u00b2 &#8211; 14x + 49)<br \/>\ny &#8211; 15 = -(x &#8211; 7)\u00b2<br \/>\ny = -(x &#8211; 7)\u00b2 + 15<br \/>\nThe vertex point is (-7, 15)<br \/>\nFrom the above vertex point,\u00a0the x-coordinate is negative<br \/>\nThe parabola closes down and the y-coordinate will be the maximum value of the given equation<br \/>\nThe given equation has a maximum value and the maximum value of the given equation is 15<\/p>\n<p>Question 45.<br \/>\nf(x) = -3x<sup>2<\/sup> &#8211; 6x &#8211; 9<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42084\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-45.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 45\" width=\"594\" height=\"397\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-45.png 594w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-45-300x201.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p>Question 46.<br \/>\nf(x) = 4x<sup>2<\/sup> &#8211; 28x + 32<br \/>\nAnswer:<br \/>\nf (x) = 4x\u00b2 &#8211; 28x + 32<br \/>\nf (x) &#8211; 32 = 4x\u00b2 &#8211; 28x + 32 &#8211; 32<br \/>\nf (x) &#8211; 32 = 4x\u00b2 &#8211; 28x<br \/>\nf (x) &#8211; 32 = 4 (x\u00b2 &#8211; 7x)<br \/>\nf (x) &#8211; 32 + \\(\\frac{49}{4}\\) =4 ( x\u00b2 &#8211; 7x + \\(\\frac{49}{4}\\))<br \/>\ny &#8211; \\(\\frac{51}{4}\\) = 4 (x &#8211; \\(\\frac{7}{2}\\))\u00b2<br \/>\ny = 4(x &#8211; \\(\\frac{7}{2}\\))\u00b2 + \\(\\frac{51}{4}\\)<br \/>\nThe vertex point is (14, \\(\\frac{51}{4}\\))<br \/>\nWe can observe that the x-coordinate is positive<br \/>\nThe parabola opens up and the y-coordinate will be the minimum value of the given equation<br \/>\nThe given equation has a minimum value and the minimum value of the given equation is \\(\\frac{51}{4}\\)<\/p>\n<p><strong>In Exercises 47\u201350, determine whether the graph could represent the function. Explain.<\/strong><br \/>\nQuestion 47.<br \/>\ny = -(x + 8)(x + 3)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35338\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-8.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 8\" width=\"137\" height=\"135\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42085\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-47.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 47\" width=\"574\" height=\"137\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-47.png 574w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-47-300x72.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 48.<br \/>\ny = (x &#8211; 5)<sup>2<\/sup><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35339\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-9.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 9\" width=\"130\" height=\"134\" \/><br \/>\nAnswer:<br \/>\ny = (x &#8211; 5)\u00b2<br \/>\ny = (x &#8211; 5) (x &#8211; 5)<br \/>\nThe vertex point for the given equation is (5, 5)<br \/>\nThe parabola closes up since the x-coordinate is positive and we will have a minimum value<br \/>\nThe minimum value will be the y-coordinate of the equation in the vertex form<br \/>\nThe given graph matches the given equation<\/p>\n<p>Question 49.<br \/>\ny = \\(\\frac{1}{4}\\)(x + 2)<sup>2<\/sup> &#8211; 4<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35340\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-10.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 10\" width=\"134\" height=\"129\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42086\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-49.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 49\" width=\"573\" height=\"141\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-49.png 573w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-49-300x74.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 50.<br \/>\ny = -2(x &#8211; 1)(x + 2)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35341\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-11.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 11\" width=\"155\" height=\"128\" \/><br \/>\nAnswer:<br \/>\ny = -2 (x &#8211; 1) (x + 2)<br \/>\nThe vertex point for the given equation is (-2, 2)<br \/>\nWe can observe that the parabola opens down since the x-coordinate is negative and we will have a maximum value.<br \/>\nThe maximum value will be the y-coordinate of the equation in the vertex form<\/p>\n<p><strong>In Exercises 51 and 52, determine which of the functions could be represented by the graph. Explain.<\/strong><br \/>\nQuestion 51.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35342\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-12.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 12\" width=\"330\" height=\"172\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-12.png 330w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-12-300x156.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42087\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-51.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 51.1\" width=\"590\" height=\"592\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-51.1.png 590w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-51.1-300x300.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-51.1-150x150.png 150w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42088\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-51.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 51.2\" width=\"557\" height=\"202\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-51.2.png 557w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-51.2-300x109.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 52.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35343\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-13.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 13\" width=\"335\" height=\"169\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-13.png 335w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-13-300x151.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe function h = -16t<sup>2<\/sup> + 48t represents the height h (in feet) of a kickball t seconds after it is kicked from the ground.<br \/>\na. Find the maximum height of the kickball.<br \/>\nb. Find and interpret the axis of symmetry.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42089\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-53.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 53\" width=\"518\" height=\"447\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-53.png 518w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-53-300x259.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou throw a stone from a height of 16 feet with an initial vertical velocity of 32 feet per second. The function h = -16t<sup>2<\/sup> + 32t + 16 represents the height h (in feet) of the stone after t seconds.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35344\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-14.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 14\" width=\"128\" height=\"213\" \/><br \/>\na. Find the maximum height of the stone.<br \/>\nAnswer:<br \/>\nHmax = h + \\(\\frac{v\u00b2}{2g}\\)<br \/>\ng = 10 m\/s<br \/>\nHmax = 16 + \\(\\frac{1024}{20}\\)<br \/>\nHmax = 67.2 feet<\/p>\n<p>b. Find and interpret the axis of symmetry.<br \/>\nAnswer:<br \/>\nh = -16t\u00b2 + 32t + 16<br \/>\nh &#8211; 16 = -16t\u00b2 + 32t + 16 &#8211; 16<br \/>\nh &#8211; 16 = -16t\u00b2 + 32t<br \/>\nh &#8211; 16 = -16 (t\u00b2 &#8211; 2t)<br \/>\nh &#8211; 16 &#8211; 16 = -16 (t\u00b2 &#8211; 2t + 1)<br \/>\nh &#8211; 32 = -16 (t &#8211; 1)\u00b2<br \/>\nh = -16 (t &#8211; 1)\u00b2 + 32<br \/>\nt = 1<\/p>\n<p>Question 55.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou are building a rectangular brick patio surrounded by a crushed stone border with a uniform width, as shown. You purchase patio bricks to cover 140 square feet. Find the width of the border.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35345\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-15.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 15\" width=\"274\" height=\"210\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42090\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-55.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 55.1\" width=\"556\" height=\"622\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-55.1.png 556w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-55.1-268x300.png 268w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42091\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-55.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 55.2\" width=\"550\" height=\"211\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-55.2.png 550w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-55.2-300x115.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou are making a poster that will have a uniform border, as shown. The total area of the poster is 722 square inches. Find the width of the border to the nearest inch.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35346\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-16.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 16\" width=\"174\" height=\"170\" \/><br \/>\nAnswer:<br \/>\nThe total area of the poster is 722 square inches<br \/>\nThe width of the poster is (28 &#8211; 2x) inches<br \/>\nThe length of the poster is (22 &#8211; 2x) inches<br \/>\nArea = Length \u00d7 Width<br \/>\n722 = (28 &#8211; 2x) (22 &#8211; 2x)<br \/>\n722 = 616 &#8211; 56x &#8211; 44x + 4x\u00b2<br \/>\n722 &#8211; 616 = 4x\u00b2 &#8211; 56x &#8211; 44x<br \/>\n106 = 4x\u00b2 &#8211; 100x<br \/>\n\\(\\frac{53}{2}\\) = x\u00b2 &#8211; 25x<br \/>\n\\(\\frac{53}{2}\\) + \\(\\frac{625}{4}\\) = x\u00b2 &#8211; 25x + \\(\\frac{625}{4}\\)<br \/>\n\\(\\frac{731}{4}\\) = (x &#8211; \\(\\frac{25}{2}\\))\u00b2<br \/>\n\u221a(x &#8211; \\(\\frac{25}{2}\\))\u00b2 = \u221a\\(\\frac{731}{4}\\)<br \/>\nx &#8211; \\(\\frac{25}{2}\\) = \u221a\\(\\frac{731}{4}\\) or x &#8211; \\(\\frac{25}{2}\\) = -\u221a\\(\\frac{731}{4}\\)<br \/>\nx = 13.62 + 12.5 or x = -13.62 + 12.5<br \/>\nx = 26.12 or x = -1.12<br \/>\nWe can observe that the width of the poster is 28 inches and the width of the poster won&#8217;t be negative<br \/>\nThe width of the border is -1.12 inches<br \/>\nThe width of the border = 28 &#8211; 2x<br \/>\n= 28 &#8211; 2 (-1.12)<br \/>\n= 30.24 inches<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong> In Exercises 57 and 58, find the value of x. Round your answer to the nearest hundredth, if necessary.<br \/>\nQuestion 57.<br \/>\nA = 108 m<sup>2<\/sup><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35347\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-17.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 17\" width=\"138\" height=\"108\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42092\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-57.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 57\" width=\"596\" height=\"608\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-57.png 596w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-57-294x300.png 294w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><\/p>\n<p>Question 58.<br \/>\nA = 288 in.<sup>2<\/sup><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35349\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-18.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 18\" width=\"171\" height=\"116\" \/><br \/>\nAnswer:<br \/>\nThe area of the rectangle = Length \u00d7 Width<br \/>\n288 = (2x + 10) (3x)<br \/>\n288 = 6x\u00b2 + 30x<br \/>\n48 = x\u00b2 + 5x<br \/>\n48 + \\(\\frac{25}{4}[latex] = x\u00b2 + 5x + [latex]\\frac{25}{4}\\)<br \/>\n54.25 = (x + \\(\\frac{5}{2}\\))\u00b2<br \/>\n\u221a(x + \\(\\frac{5}{2}\\))\u00b2 = \u221a54.25<br \/>\n\u221a54.25 = 7.36<br \/>\nx + \\(\\frac{5}{2}\\) = 7.36 or x + \\(\\frac{5}{2}\\) = -7.36<br \/>\nx = 7.36 &#8211; 2.5 or x = -7.36 &#8211; 2.5<br \/>\nx = 4.86 or x = -9.86<br \/>\nThe length and width won&#8217;t be negative<br \/>\nx = 4.86<\/p>\n<p><strong>In Exercises 59\u201362, solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.<\/strong><br \/>\nQuestion 59.<br \/>\n0.5x<sup>2<\/sup> + x &#8211; 2 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42093\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-59.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 59\" width=\"409\" height=\"497\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-59.png 409w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-59-247x300.png 247w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/><\/p>\n<p>Question 60.<br \/>\n0.75x<sup>2<\/sup> + 1.5x = 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115075\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-72.png\" alt=\"\" width=\"732\" height=\"669\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-72.png 732w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-72-300x274.png 300w\" sizes=\"(max-width: 732px) 100vw, 732px\" \/><\/p>\n<p>Question 61.<br \/>\n\\(\\frac{8}{3}\\) x &#8211; \\(\\frac{2}{3}\\)x<sup>2<\/sup> = &#8211;\\(\\frac{5}{6}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42094\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-61.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 61\" width=\"394\" height=\"699\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-61.png 394w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-61-169x300.png 169w\" sizes=\"(max-width: 394px) 100vw, 394px\" \/><\/p>\n<p>Question 62.<br \/>\n\\(\\frac{1}{4}\\)x<sup>2<\/sup> + \\(\\frac{1}{2}\\)x &#8211; \\(\\frac{5}{4}\\) = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115076\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-73.png\" alt=\"\" width=\"757\" height=\"1001\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-73.png 757w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-73-227x300.png 227w\" sizes=\"(max-width: 757px) 100vw, 757px\" \/><\/p>\n<p>Question 63.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nThe distance d (in feet) that it takes a car to come to a complete stop can be modeled by d = 0.05s<sup>2<\/sup> + 2.2s, where s is the speed of the car (in miles per hour). A car has 168 feet to come to a complete stop. Find the maximum speed at which the car can travel.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42095\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-63.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 63\" width=\"574\" height=\"544\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-63.png 574w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-63-300x284.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 64.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nDuring a \u201cbig air\u201d competition, snowboarders launch themselves from a half-pipe, perform tricks in the air, and land back in the half-pipe. The height h (in feet) of a snowboarder above the bottom of the half-pipe can be modeled by h = -16t<sup>2<\/sup> + 24t + 16.4, where t is the time (in seconds) after the snowboarder launches into the air. The snowboarder lands 3.2 feet lower than the height of the launch. How long is the snowboarder in the air? Round your answer to the nearest tenth of a second.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35350\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-19.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 19\" width=\"266\" height=\"181\" \/><br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou have 80 feet of fencing to make a rectangular horse pasture that covers 750 square feet. A barn will be used as one side of the pasture, as shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35351\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-20.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 20\" width=\"197\" height=\"137\" \/><br \/>\na. Write equations for the amount of fencing to be used and the area enclosed by the fencing.<br \/>\nb. Use substitution to solve the system of equations from part (a). What are the possible dimensions of the pasture?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42096\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-65.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 65.1\" width=\"643\" height=\"406\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-65.1.png 643w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-65.1-300x189.png 300w\" sizes=\"(max-width: 643px) 100vw, 643px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42097\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-65.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 65.2\" width=\"686\" height=\"619\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-65.2.png 686w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-65.2-300x271.png 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Question 66.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph represents the quadratic function y = x<sup>2<\/sup> &#8211; 4x + 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35352\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-21.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 21\" width=\"160\" height=\"159\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-21.png 160w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-21-150x150.png 150w\" sizes=\"(max-width: 160px) 100vw, 160px\" \/><br \/>\na. Use the graph to estimate the x-values for which y = 3.<br \/>\nAnswer:<br \/>\ny = x\u00b2 &#8211; 4x + 6<br \/>\ny = 3<br \/>\nx\u00b2 &#8211; 4x + 6 = 3<br \/>\nx\u00b2 &#8211; 4x = 3 &#8211; 6<br \/>\nx\u00b2 &#8211; 4x = -3<br \/>\nx\u00b2 &#8211; 4x + 4 = -3 + 4<br \/>\n(x &#8211; 2)\u00b2 = 1<br \/>\n\u221a(x &#8211; 2)\u00b2 = \u221a1<br \/>\nx &#8211; 2 = 1 or x &#8211; 2 = -1<br \/>\nx = 1 + 2 or x = -1 + 2<br \/>\nx = 3 or x = 1<\/p>\n<p>b. Explain how you can use the method of completing the square to check your estimates in part (a).<br \/>\nAnswer:<br \/>\nThe steps to &#8220;Completing the Square&#8221; to check the estimates in part (a) are:<br \/>\n1. Divide all terms by a (The coefficient of x\u00b2)<br \/>\n2. Move the number term (c \/ a) to the right side of the equation<br \/>\n3. Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation<\/p>\n<p>Question 67.<br \/>\n<strong>COMPARING METHODS<\/strong><br \/>\nConsider the quadratic equation x<sup>2<\/sup> + 12x + 2 = 12.<br \/>\na. Solve the equation by graphing.<br \/>\nb. Solve the equation by completing the square.<br \/>\nc. Compare the two methods. Which do you prefer? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42098\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-67.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 67.1\" width=\"548\" height=\"573\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-67.1.png 548w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-67.1-287x300.png 287w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42099\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-67.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 67.2\" width=\"560\" height=\"321\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-67.2.png 560w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-67.2-300x172.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 68.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nSketch the graph of the equation x<sup>2<\/sup> &#8211; 2xy + y<sup>2<\/sup> &#8211; x &#8211; y = 0. Identify the graph.<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 2xy + y\u00b2 &#8211; x &#8211; y = 0<br \/>\nx\u00b2 + y\u00b2 + 2gx + 2fy + 2hxy + c = 0<br \/>\nThe graph of the given equation looks like a circle<\/p>\n<p>Question 69.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe product of two consecutive even integers that are positive is 48. Write and solve an equation to find the integers.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42100\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-69.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 69\" width=\"567\" height=\"491\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-69.png 567w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-69-300x260.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 70.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe product of two consecutive odd integers that are negative is 195. Write and solve an equation to find the integers.<br \/>\nAnswer:<br \/>\n(1 &#8211; n) (3 &#8211; n) = 195<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115077\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-74.png\" alt=\"\" width=\"424\" height=\"400\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-74.png 424w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-74-300x283.png 300w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><\/p>\n<p>Question 71.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYou purchase stock for $16 per share. You sell the stock 30 days later for $23.50 per share. The price y (in dollars) of a share during the 30-day period can be modeled by y = -0.025x<sup>2<\/sup> + x + 16, where x is the number of days after the stock is purchased. Your friend says you could have sold the stock earlier for $23.50 per share. Is your friend correct? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35353\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-22.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 22\" width=\"270\" height=\"135\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42101\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-71.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 71\" width=\"590\" height=\"627\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-71.png 590w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-71-282x300.png 282w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 72.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou are solving the equation x<sup>2<\/sup> + 9x =18. What are the advantages of solving the equation by completing the square instead of using other methods you have learned?<br \/>\nAnswer:<br \/>\nx\u00b2 + 9x = 18<br \/>\nx\u00b2 + 2( \\(\\frac{9}{2}\\) )x = 18<br \/>\nTo make the expression present on the left side a factor trinomial to get the exact values of x, we have to use the &#8220;Completing the squares&#8221; method<br \/>\nWhen we use the graphing method,<br \/>\nWe won&#8217;t get the exact values of x for the equation<br \/>\nWe can conclude that we have to solve the above equation by using the &#8220;Completing the squares&#8221; method to get the exact values of x when we compared it with the other methods<\/p>\n<p>Question 73.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nYou are knitting a rectangular scarf. The pattern results in a scarf that is 60 inches long and 4 inches wide. However, you have enough yarn to knit 396 square inches. You decide to increase the dimensions of the scarf so that you will use all your yarn. The increase in the length is three times the increase in the width. What are the dimensions of your scarf?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35354\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-23.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 23\" width=\"298\" height=\"184\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42102\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-73.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 73.1\" width=\"552\" height=\"551\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-73.1.png 552w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-73.1-300x300.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-73.1-150x150.png 150w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42103\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-73.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 73.2\" width=\"579\" height=\"315\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-73.2.png 579w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-73.2-300x163.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 74.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow many solutions does x<sup>2<\/sup> + bx = c have when c &lt; -(\\(\\frac{b}{2}\\))<sup>2<\/sup> ? Explain.<br \/>\nAnswer:<br \/>\nx\u00b2 + bx = c<br \/>\nx\u00b2 + bx + \\(\\frac{b\u00b2}{4}\\) = c + \\(\\frac{b\u00b2}{4}\\)<br \/>\n(x + \\(\\frac{b}{2}\\))\u00b2 = c +c + \\(\\frac{b\u00b2}{4}\\)<br \/>\nc &lt; &#8211; \\(\\frac{b\u00b2}{4}\\)<br \/>\nWhen c &lt; &#8211; \\(\\frac{b\u00b2}{4}\\), the square value will also be negative<br \/>\nBut, we know that the square won&#8217;t take any negative values<br \/>\nThe number of solutions of x\u00b2 + bx = c when c &lt;- \\(\\frac{b\u00b2}{4}\\) are: 0<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Write a recursive rule for the sequence.<\/strong><br \/>\nQuestion 75.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35355\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-24.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 24\" width=\"121\" height=\"151\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42104\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-75.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 75\" width=\"650\" height=\"114\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-75.png 650w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-75-300x53.png 300w\" sizes=\"(max-width: 650px) 100vw, 650px\" \/><\/p>\n<p>Question 76.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35356\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-25.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 25\" width=\"133\" height=\"148\" \/><br \/>\nAnswer:<br \/>\nThe first term is 3 (When x = 1)<br \/>\nEach term is obtained by multiplying the previous term by 2<br \/>\nThe recursive rule for the sequence is a1 = an-1 \u00d7 2<\/p>\n<p>Question 77.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35357\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-26.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 26\" width=\"129\" height=\"147\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42105\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-77.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 77\" width=\"563\" height=\"86\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-77.png 563w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-77-300x46.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Simplify the expression \\(\\sqrt{b^{2}-4 a c}\\) for the given values.<br \/>\nQuestion 78.<br \/>\na = 3, b = -6, c = 2<br \/>\nAnswer:<br \/>\n\\(\\sqrt{b\u00b2 &#8211; 4ac}\\)<br \/>\na = 3, b = -6, and c = 2<br \/>\n\\(\\sqrt{b\u00b2 &#8211; 4ac}\\)<br \/>\n= \\(\\sqrt{(-6)\u00b2 &#8211; 4 (3) (2)}\\)<br \/>\n= \\(\\sqrt{36 &#8211; 24}\\)<br \/>\n= \\(\\sqrt{12}\\)<br \/>\n= \\(\\sqrt{4 \u00d7 3}\\)<br \/>\n= 2\\(\\sqrt{3}\\)<\/p>\n<p>Question 79.<br \/>\na = -2, b = 4, c = 7<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42106\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-79.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 79\" width=\"293\" height=\"206\" \/><\/p>\n<p>Question 80.<br \/>\na = 1, b = 6, c = 4<br \/>\nAnswer:<br \/>\n\\(\\sqrt{b\u00b2 &#8211; 4ac}\\)<br \/>\na = 1, b = 6, and c = 4<br \/>\n\\(\\sqrt{b\u00b2 &#8211; 4ac}\\)<br \/>\n= \\(\\sqrt{(6)\u00b2 &#8211; 4 (1) (4)}\\)<br \/>\n= \\(\\sqrt{36 &#8211; 16}\\)<br \/>\n= \\(\\sqrt{20}\\)<br \/>\n= \\(\\sqrt{4 \u00d7 5}\\)<br \/>\n= 2\\(\\sqrt{5}\\)<\/p>\n<h3><a id=\"Lesson_9.5_Solving_Quadratic_Equations_Using_the_Quadratic_Formula\"><\/a>Lesson 9.5 Solving Quadratic Equations Using the Quadratic Formula<\/h3>\n<p><strong>Essential Question<\/strong> How can you derive a formula that can be used to write the solutions of any quadratic equation in standard form?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Deriving the Quadratic Formula<br \/>\nWork with a partner. The following steps show a method of solving ax<sup>2<\/sup> + bx + c = 0. Explain what was done in each step.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35358\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 1\" width=\"465\" height=\"386\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-1.png 465w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-1-300x249.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><br \/>\nAnswer:<br \/>\n1. Write the equation<br \/>\n2. Multiply with &#8220;4a&#8221; on both sides<br \/>\n3. Add b\u00b2 on both sides<br \/>\n4. Subtract with &#8220;4ac&#8221; on both sides<br \/>\n5. Write the expression that is present on the left side i.e., in the form of a trinomial i.e., (x \u00b1 a)\u00b2<br \/>\n6. Take &#8220;Square root&#8221; on both sides<br \/>\n7. Subtract with &#8220;b&#8221; on both sides<br \/>\n8. Divide by &#8220;2a&#8221; into both sides<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Deriving the Quadratic Formula by Completing the Square<br \/>\nWork with a partner.<br \/>\na. Solve ax<sup>2<\/sup> + bx + c = 0 by completing the square. (Hint: Subtract c from each side, divide each side by a, and then proceed by completing the square.)<br \/>\nAnswer:<br \/>\nax\u00b2 + bx + c = 0<br \/>\nax\u00b2 + bx + c &#8211; c = 0 &#8211; c<br \/>\nax\u00b2 + bx = -c<br \/>\nx\u00b2 + \\(\\frac{b}{a}\\)x = &#8211;\\(\\frac{c}{a}\\)<br \/>\nx\u00b2 + \\(\\frac{b}{a}\\) + \\(\\frac{b\u00b2}{4a\u00b2}\\) = &#8211;\\(\\frac{c}{a}\\) + \\(\\frac{b\u00b2}{4a\u00b2}\\)<br \/>\n(x + \\(\\frac{b}{2a}\\))\u00b2 = \\(\\frac{-4c + b\u00b2}{4a\u00b2}\\)<br \/>\n\u221a(x + \\(\\frac{b}{2a}\\))\u00b2 = \u221a\\(\\frac{-4c + b\u00b2}{4a\u00b2}\\)<br \/>\nx + \\(\\frac{b}{2a}\\) = \\(\\frac{\\sqrt{-4c + b\u00b2}}{2a}\\) or x + \\(\\frac{b}{2a}\\) = &#8211;\\(\\frac{\\sqrt{-4c + b\u00b2}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\) or x =\u00a0 &#8211;\\(\\frac{b}{2a}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<\/p>\n<p>b. Compare this method with the method in Exploration 1. Explain why you think 4a and b<sup>2<\/sup> were chosen in Steps 2 and 3 of Exploration 1.<br \/>\nAnswer:<br \/>\nIn Exploration 1,<br \/>\nWe add 4a to make the expression on the left side of a factor trinomial<br \/>\nWe add b\u00b2 to make the factor trinomial complete i.e., to make the expression on the left side in the form of a\u00b2 + 2ab + b\u00b2<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you derive a formula that can be used to write the solutions of any quadratic equation in standard form?<br \/>\nAnswer:<br \/>\nThe formula can be actually derived using the steps involved in completing the square.<br \/>\nIt stems from the fact that any quadratic\u00a0function or\u00a0equation\u00a0of the form<br \/>\ny = ax\u00b2 + b x + c can be solved for its roots.<\/p>\n<p>Question 4.<br \/>\nUse the Quadratic Formula to solve each quadratic equation.<br \/>\na. x<sup>2<\/sup> + 2x &#8211; 3 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 + 2x &#8211; 3 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = 2, and c = -3<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\) and x =\u00a0 &#8211;\\(\\frac{b}{2a}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{2}{2 (1)}\\) + \\(\\frac{\\sqrt{2\u00b2 &#8211; 4 (1) (-3)}}{2 (1)}\\)<br \/>\nx = -1 + \\(\\frac{\\sqrt{4 + 12}}{2}\\)<br \/>\nx= -1 + 2<br \/>\nx = 1<br \/>\nx =\u00a0 &#8211;\\(\\frac{b}{2a}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{2}{2 (1)}\\) &#8211; \\(\\frac{\\sqrt{2\u00b2 &#8211; 4 (1) (-3)}}{2 (1)}\\)<br \/>\nx = -1 &#8211; \\(\\frac{\\sqrt{4 + 12}}{2}\\)<br \/>\nx= -1 &#8211; 2<br \/>\nx = -3<\/p>\n<p>b. x<sup>2<\/sup> &#8211; 4x + 4 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 4x + 4 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = -4, and c = 4<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\) and x =\u00a0 &#8211;\\(\\frac{b}{2a}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{-4}{2 (1)}\\) + \\(\\frac{\\sqrt{(-4)\u00b2 &#8211; 4 (1) (4)}}{2 (1)}\\)<br \/>\nx = 2 + \\(\\frac{\\sqrt{16 &#8211; 16}}{2}\\)<br \/>\nx= 2<br \/>\nx =\u00a0 &#8211;\\(\\frac{-4}{2 (1)}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = 2 &#8211; \\(\\frac{\\sqrt{(-4)\u00b2 &#8211; 4 (1) (4)}}{2 (1)1}\\)<br \/>\nx = 2 &#8211; \\(\\frac{\\sqrt{16 &#8211; 16}}{2}\\)<br \/>\nx = 2<\/p>\n<p>c. x<sup>2<\/sup> + 4x + 5 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 + 4x + 5 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = 4, and c = 5<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\) and x =\u00a0 &#8211;\\(\\frac{b}{2a}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{4}{2 (1)}\\) + \\(\\frac{\\sqrt{(4)\u00b2 &#8211; 4 (1) (5)}}{2 (1)}\\)<br \/>\nx = -2 + \\(\\frac{\\sqrt{16 &#8211; 20}}{2}\\)<br \/>\nx= -2 + i<br \/>\nx =\u00a0 &#8211;\\(\\frac{4}{2 (1)}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = -2 &#8211; \\(\\frac{\\sqrt{(4)\u00b2 &#8211; 4 (1) (5)}}{2 (1)}\\)<br \/>\nx = -2 &#8211; \\(\\frac{\\sqrt{16 &#8211; 20}}{2}\\)<br \/>\nx= -2 &#8211; i<br \/>\nThe solutions of the given equation are: -2 \u00b1 i<\/p>\n<p>Question 5.<br \/>\nUse the Internet to research imaginary numbers. How are they related to quadratic equations?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35359\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 2\" width=\"224\" height=\"155\" \/><br \/>\nAnswer:<br \/>\nAn &#8220;Imaginary number&#8221; is a number that, when squared, has a negative result. Essentially, an\u00a0imaginary number\u00a0is the square root of a negative\u00a0number and does not have a tangible value.\u00a0 Imaginary numbers are usually denoted by the symbol i<br \/>\n\u221a-1 = i<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the equation using the Quadratic Formula. Round your solutions to the nearest tenth, if necessary.<\/strong><br \/>\nQuestion 1.<br \/>\nx<sup>2<\/sup> &#8211; 6x + 5 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 6x + 5 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = -6, and c = 5<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\) and x =\u00a0 &#8211;\\(\\frac{b}{2a}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{6}{2 (1)}\\) + \\(\\frac{\\sqrt{(-6)\u00b2 &#8211; 4 (1) (5)}}{2 (1)}\\)<br \/>\nx = 3 + \\(\\frac{\\sqrt{36 &#8211; 20}}{2}\\)<br \/>\nx= 3 + 2<br \/>\nx = 5<br \/>\nx =\u00a0 \\(\\frac{6}{2 (1)}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = 3 &#8211; \\(\\frac{\\sqrt{(-6)\u00b2 &#8211; 4 (1) (5)}}{2 (1)}\\)<br \/>\nx = 3 &#8211; \\(\\frac{\\sqrt{36 &#8211; 20}}{2}\\)<br \/>\nx= 3 &#8211; 2<br \/>\nx = 1<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{1}{2}\\)x<sup>2<\/sup> + x &#8211; 10 = 0<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{2}\\)x\u00b2 + x &#8211; 10 = 0<br \/>\nx\u00b2 + 2x &#8211; 20 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = 2, and c = -20<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\) and x =\u00a0 &#8211;\\(\\frac{b}{2a}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{2}{2 (1)}\\) + \\(\\frac{\\sqrt{(2)\u00b2 + 4 (1) (20)}}{2 (1)}\\)<br \/>\nx = -1 + \\(\\frac{\\sqrt{84}}{2}\\)<br \/>\nx= 3.5<br \/>\nx =\u00a0 &#8211;\\(\\frac{2}{2 (1)}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = -1 &#8211; \\(\\frac{\\sqrt{(2)\u00b2 + 4 (1) (20)}}{2 (1)}\\)<br \/>\nx = -1 &#8211; \\(\\frac{\\sqrt{84}}{2}\\)<br \/>\nx= -4.5<\/p>\n<p>Question 3.<br \/>\n-3x<sup>2<\/sup> + 2x + 7 = 0<br \/>\nAnswer:<br \/>\n-3x\u00b2 + 2x + 7 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = -3, b = 2, and c = 7<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\) and x =\u00a0 &#8211;\\(\\frac{b}{2a}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{2}{2 (3)}\\) + \\(\\frac{\\sqrt{(2)\u00b2 + 4 (3) (7)}}{2 (-3)}\\)<br \/>\nx = \\(\\frac{1}{3}\\) + \\(\\frac{\\sqrt{88}}{-6}\\)<br \/>\nx= -1.2<br \/>\nx =\u00a0 \\(\\frac{2}{2 (3)}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{1}{3}\\) &#8211; \\(\\frac{\\sqrt{(2)\u00b2 + 4 (3) (7)}}{2 (-3)}\\)<br \/>\nx = \\(\\frac{1}{3}\\) + \\(\\frac{\\sqrt{88}}{6}\\)<br \/>\nx= 1.8<\/p>\n<p>Question 4.<br \/>\n4x<sup>2<\/sup> &#8211; 4x = -1<br \/>\nAnswer:<br \/>\n4x\u00b2 &#8211; 4x = -1<br \/>\n4x\u00b2 &#8211; 4x + 1 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 4, b = -4, and c = 1<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\) and x =\u00a0 &#8211;\\(\\frac{b}{2a}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{4}{2 (4)}\\) + \\(\\frac{\\sqrt{(-4)\u00b2 &#8211; 4 (1) (4)}}{2 (4)}\\)<br \/>\nx = \\(\\frac{1}{2}\\) + \\(\\frac{\\sqrt{16 &#8211; 16}}{8}\\)<br \/>\nx= \\(\\frac{1}{2}\\)<br \/>\nx =\u00a0 \\(\\frac{4}{2 (4)}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{1}{2}\\) &#8211; \\(\\frac{\\sqrt{(-4)\u00b2 &#8211; 4 (1) (4)}}{2 (4)}\\)<br \/>\nx = \\(\\frac{1}{2}\\) &#8211; \\(\\frac{\\sqrt{16 &#8211; 16}}{8}\\)<br \/>\nx= \\(\\frac{1}{2}\\)<\/p>\n<p>Question 5.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nWhen were there about 60 wolf breeding pairs?<br \/>\nAnswer:<br \/>\nThe given quadratic equation that used to model the wolf pairs for x years is:<br \/>\ny = 0.20x\u00b2 + 1.8x &#8211; 3<br \/>\n0.20x\u00b2 + 1.8x &#8211; 3 = 60<br \/>\n0.20x\u00b2 + 1.8x &#8211; 63 =\u00a0 0<br \/>\nx\u00b2 + 9x &#8211; 315 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = 9, and c = -315<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\) and x =\u00a0 &#8211;\\(\\frac{b}{2a}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{b}{2a}\\) + \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{9}{2 (1)}\\) + \\(\\frac{\\sqrt{(9)\u00b2 + 4 (1) (315)}}{2 (1)}\\)<br \/>\nx = &#8211;\\(\\frac{9}{2}\\) + \\(\\frac{\\sqrt{1,341}}{2}\\)<br \/>\nx= 13.80<br \/>\nx = 14<br \/>\nx =\u00a0 &#8211;\\(\\frac{9}{2 (1)}\\) &#8211; \\(\\frac{\\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = &#8211;\\(\\frac{9}{2}\\) &#8211; \\(\\frac{\\sqrt{(9)\u00b2 + 4 (1) (315)}}{2 (1)}\\)<br \/>\nx = &#8211;\\(\\frac{9}{2}\\) &#8211; \\(\\frac{\\sqrt{1,341}}{2}\\)<br \/>\nx= -22.8<br \/>\n= -23<br \/>\nSince x represents the number of years, the number of years won&#8217;t be negative<br \/>\nx = 14 years<br \/>\nAfter 14 years, i.e, in 2004, there were 60 wolf-breeding pairs<\/p>\n<p>Question 6.<br \/>\nThe number y of bald eagle nesting pairs in state x years since 2000 can be modeled by the function y = 0.34x<sup>2<\/sup> + 13.1x + 51.<br \/>\na. When were there about 160 bald eagle nesting pairs?<br \/>\nAnswer:<br \/>\ny = 0.34x\u00b2 + 13.1x + 51<br \/>\ny =160<br \/>\n160 = 0.34x\u00b2 + 13.1x + 51<br \/>\n0.34x\u00b2 + 13.1x &#8211; 109 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115227\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-75.png\" alt=\"\" width=\"582\" height=\"387\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-75.png 582w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-75-300x199.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><br \/>\nSince x is the number of years, the value of x won&#8217;t be negative<br \/>\nx = 7.03 years<br \/>\nx = 7 years<br \/>\nWe can conclude that after 7 years from 2000, i.e., in 2007, there were 160 bald eagle nesting pairs<\/p>\n<p>b. How many bald eagle nesting pairs were there in 2000?<br \/>\nAnswer:<br \/>\nThere are 160 bald eagle nesting pairs in 2007<br \/>\nTo find the number of bald eagle nesting pairs in 2000,<br \/>\nSubtract the number of bald eagle nesting pairs in 2007 from the difference between 2000 and 2007<br \/>\nThe number of bald eagles nesting pairs in 2000 = 160 &#8211; (2007 &#8211; 2000)<br \/>\n= 160 &#8211; 7<br \/>\n= 153<\/p>\n<p><strong>Determine the number of real solutions of the equation.<\/strong><br \/>\nQuestion 7.<br \/>\n-x<sup>2<\/sup> + 4x &#8211; 4 = 0<br \/>\nAnswer:<br \/>\n-x\u00b2 + 4x &#8211; 4 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = -1, b = 4, and c = -4<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then there will be 2 real solutions<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then there will be one real solution<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then there are no real solutions<br \/>\nb\u00b2 &#8211; 4ac = 4\u00b2 &#8211; 4 (-1) (-4)<br \/>\n= 16 &#8211; 16<br \/>\n= 0<br \/>\nThere will be only 1 solution for the given equation<\/p>\n<p>Question 8.<br \/>\n6x<sup>2<\/sup> + 2x = -1<br \/>\nAnswer:<br \/>\n6x\u00b2 + 2x = -1<br \/>\n6x\u00b2 + 2x + 1 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 6, b = 2, and c = 1<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then there will be 2 real solutions<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then there will be one real solution<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then there are no real solutions<br \/>\nb\u00b2 &#8211; 4ac = 2\u00b2 &#8211; 4 (6) (1)<br \/>\n= 4 &#8211; 24<br \/>\n= -20<br \/>\nThere are no real solutions for the given equation<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{1}{2}\\)x<sup>2<\/sup> = 7x &#8211; 1<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{2}\\)x\u00b2 = 7x &#8211; 1<br \/>\n\\(\\frac{1}{2}\\)x\u00b2 &#8211; 7x + 1= 0<br \/>\nx\u00b2 &#8211; 14x + 2 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = -14, and c = 2<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then there will be 2 real solutions<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then there will be one real solution<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then there are no real solutions<br \/>\nb\u00b2 &#8211; 4ac = (-14)\u00b2 &#8211; 4 (1) (2)<br \/>\n= 196 &#8211; 8<br \/>\n= 188<br \/>\nThere are 2 solutions for the given equation<\/p>\n<p><strong>Find the number of x-intercepts of the graph of the function.<\/strong><br \/>\nQuestion 10.<br \/>\ny = -x<sup>2<\/sup> + x &#8211; 6<br \/>\nAnswer:<br \/>\ny = -x\u00b2 + x &#8211; 6<br \/>\n-x\u00b2 + x &#8211; 6 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = -1, b = 1, and c = -6<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then there will be 2 x- intercepts<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then there will be one x-intercept<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then there are no x-intercepts<br \/>\nb\u00b2 &#8211; 4ac = 1\u00b2 &#8211; 4 (-1) (-6)<br \/>\n= 1 &#8211; 24<br \/>\n= -23<br \/>\nThere are no x-intercepts for the given equation<\/p>\n<p>Question 11.<br \/>\ny = x<sup>2<\/sup> &#8211; x<br \/>\nAnswer:<br \/>\ny = x\u00b2 &#8211; x<br \/>\nx\u00b2 &#8211; x = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = -1, and c = 0<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then there will be 2 x- intercepts<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then there will be one x-intercept<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then there are no x-intercepts<br \/>\nb\u00b2 &#8211; 4ac = (-1)\u00b2 &#8211; 4 (1) (0)<br \/>\n= 1 &#8211; 0<br \/>\n= 1<br \/>\nThere are 2 x-intercepts for the given equation<\/p>\n<p>Question 12.<br \/>\nf(x) = x<sup>2<\/sup> + 12x + 36<br \/>\nAnswer:<br \/>\nf (x) = x\u00b2 + 12x + 36<br \/>\nx\u00b2 + 12x + 36 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = 12, and c = 36<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then there will be 2 x- intercepts<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then there will be one x-intercept<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then there are no x-intercepts<br \/>\nb\u00b2 &#8211; 4ac = 12\u00b2 &#8211; 4 (1) (36)<br \/>\n= 144 &#8211; 144<br \/>\n= 0<br \/>\nThere is only 1 x-intercept for the given equation<\/p>\n<p><strong>Solve the equation using any method. Explain your choice of method.<\/strong><br \/>\nQuestion 13.<br \/>\nx<sup>2<\/sup> + 11x &#8211; 12 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 + 11x &#8211; 12 = 0<br \/>\nx\u00b2 + 12x &#8211; x &#8211; 12 = 0<br \/>\nx (x + 12) &#8211; 1 (x + 12) = 0<br \/>\n(x &#8211; 1) (x + 2) = 0<br \/>\nx &#8211; 1 = 0 or x + 12 = 0<br \/>\nx = 1 or x = -12<\/p>\n<p>Question 14.<br \/>\n9x<sup>2<\/sup> &#8211; 5 = 4<br \/>\nAnswer:<br \/>\n9x\u00b2 &#8211; 5 = 4<br \/>\n9x\u00b2 = 4 + 5<br \/>\n9x\u00b2 = 9<br \/>\nx\u00b2 = \\(\\frac{9}{9}\\)<br \/>\nx\u00b2 = 1<br \/>\nx\u00b2 = d<br \/>\n\u221ax\u00b2 = \u221a1<br \/>\nx = 1 or x = -1<\/p>\n<p>Question 15.<br \/>\n5x<sup>2<\/sup> &#8211; x &#8211; 1 = 0<br \/>\nAnswer:<br \/>\n5x\u00b2 &#8211; x &#8211; 1 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 5, b = -1, and c = -1<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{1 \u00b1 \\sqrt{(-1)\u00b2 + 4 (1) (5)}}{2 (5)}\\)<br \/>\nx = \\(\\frac{1 \u00b1 \\sqrt{21}}{10}\\)<\/p>\n<p>Question 16.<br \/>\nx<sup>2<\/sup> = 2x &#8211; 5<br \/>\nAnswer:<br \/>\nx\u00b2 = 2x &#8211; 5<br \/>\nx\u00b2 &#8211; 2x = 5<br \/>\nx\u00b2 &#8211; 2x + 1 = 5 + 1<br \/>\n(x &#8211; 1)\u00b2 = 6<br \/>\n\u221a(x &#8211; 1)\u00b2 = \u221a6<br \/>\nx &#8211; 1 = \u221a6 or x &#8211; 1 = -\u221a6<br \/>\nx = \u221a6 + 1 or x = -\u221a6 + 1<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Using_the_Quadratic_Formula_9.5_Exercises\"><\/a>Solving Quadratic Equations Using the Quadratic Formula 9.5 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat formula can you use to solve any quadratic equation? Write the formula.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42107\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 1\" width=\"550\" height=\"91\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-1.png 550w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-1-300x50.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nIn the Quadratic Formula, what is the discriminant? What does the value of the discriminant determine?<br \/>\nAnswer:<br \/>\nThe quadratic formula is<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nThe discriminant is: b\u00b2 &#8211; 4ac<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then there will be 2 real solutions<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then there will be one real solution<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then there are no real solutions<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p>In Exercises 3\u20138, write the equation in standard form. Then identify the values of a, b, and c that you would use to solve the equation using the Quadratic Formula.<br \/>\nQuestion 3.<br \/>\nx<sup>2<\/sup> = 7x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42108\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-3.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 3\" width=\"531\" height=\"162\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-3.png 531w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-3-300x92.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 4.<br \/>\nx<sup>2<\/sup> &#8211; 4x = -12<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 4x = -12<br \/>\nx\u00b2 &#8211; 4x + 12 = 12 &#8211; 12<br \/>\nx\u00b2 &#8211; 4x + 12 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = -4, and c = 12<br \/>\nx\u00b2 &#8211; 4x + 4x = -12 + 4x<br \/>\nx\u00b2 = -12 + 4x<br \/>\nx\u00b2 &#8211; x\u00b2 = -12 + 4x &#8211; x\u00b2<br \/>\n-12 + 4x &#8211; x\u00b2 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = -1, b = 4, and c = -12<\/p>\n<p>Question 5.<br \/>\n-2x<sup>2<\/sup> + 1 = 5x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42109\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-5.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 5\" width=\"382\" height=\"308\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-5.png 382w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-5-300x242.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><\/p>\n<p>Question 6.<br \/>\n3x + 2 = 4x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<span style=\"text-decoration: underline;\">Method 1:<\/span><br \/>\n3x + 2 = 4x\u00b2<br \/>\n3x + 2 &#8211; 2 = 4x\u00b2 &#8211; 2<br \/>\n3x &#8211; 3x = 4x\u00b2 &#8211; 2 &#8211; 3x<br \/>\n4x\u00b2 &#8211; 3x &#8211; 2 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 4, b = -3, and c = -2<br \/>\n<span style=\"text-decoration: underline;\">Method 2:<\/span><br \/>\n3x + 2 &#8211; 4x\u00b2 = 4x\u00b2 &#8211; 4x\u00b2<br \/>\n-4x\u00b2 + 3x + 2 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = -4, b = 3, and c = 2<\/p>\n<p>Question 7.<br \/>\n4 &#8211; 3x = -x<sup>2<\/sup> + 3x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42110\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-7.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 7\" width=\"388\" height=\"308\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-7.png 388w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-7-300x238.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/p>\n<p>Question 8.<br \/>\n-8x &#8211; 1 = 3x<sup>2<\/sup> + 2<br \/>\nAnswer:<br \/>\n-8x &#8211; 1 = 3x\u00b2 + 2<br \/>\n-8x -1 &#8211; 2 = 3x\u00b2<br \/>\n-8x &#8211; 3 = 3x\u00b2<br \/>\nMethod 1:<br \/>\n-8x &#8211; 3 + 3 = 3x\u00b2 + 3<br \/>\n-8x = 3x\u00b2 + 3<br \/>\n8x &#8211; 8x = 3x\u00b2 + 3 + 8x<br \/>\n3x\u00b2 + 8x + 3 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 3, b = 8, and c = 3<br \/>\nMethod 2:<br \/>\n-8x &#8211; 3 &#8211; 3x\u00b2 = 3x\u00b2 &#8211; 3x\u00b2<br \/>\n-3x\u00b2 &#8211; 8x &#8211; 3 = 0<br \/>\n3x\u00b2 + 8x + 3 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 3, b = 8, and c = 3<\/p>\n<p><strong>In Exercises 9\u201322, solve the equation using the Quadratic Formula. Round your solutions to the nearest tenth, if necessary.<\/strong><br \/>\nQuestion 9.<br \/>\nx<sup>2<\/sup> &#8211; 12x + 36 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42111\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-9.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 9\" width=\"466\" height=\"400\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-9.png 466w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-9-300x258.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/p>\n<p>Question 10.<br \/>\nx<sup>2<\/sup> + 7x + 16 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 + 7x + 16 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = 7, and c = 16<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{-7 \u00b1 \\sqrt{(7)\u00b2 &#8211; 4 (1) (16)}}{2 (1)}\\)<br \/>\nx = \\(\\frac{-7 \u00b1 \\sqrt{-15}}{2}\\)<br \/>\nx = \\(\\frac{-7 \u00b1 15i}{2}\\)<\/p>\n<p>Question 11.<br \/>\nx<sup>2<\/sup> &#8211; 10x &#8211; 11 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42112\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-11.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 11\" width=\"481\" height=\"480\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-11.png 481w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-11-300x300.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-11-150x150.png 150w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>Question 12.<br \/>\n2x<sup>2<\/sup> &#8211; x &#8211; 1 = 0<br \/>\nAnswer:<br \/>\n2x\u00b2 &#8211; x &#8211; 1 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 2, b = -1, and c = -1<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{1 \u00b1 \\sqrt{(-1)\u00b2 + 4 (1) (2)}}{2 (2)}\\)<br \/>\nx = \\(\\frac{1 \u00b1 \\sqrt{9}}{4}\\)<br \/>\nx = \\(\\frac{1 \u00b1 3}{4}\\)<br \/>\nx = \\(\\frac{1 + 3}{4}\\) or x = \\(\\frac{1 &#8211; 3}{4}\\)<br \/>\nx = 1 or x = &#8211;\\(\\frac{1}{2}\\)<\/p>\n<p>Question 13.<br \/>\n2x<sup>2<\/sup> &#8211; 6x + 5 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42113\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-13.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 13\" width=\"560\" height=\"339\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-13.png 560w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-13-300x182.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 14.<br \/>\n9x<sup>2<\/sup> &#8211; 6x + 1 = 0<br \/>\nAnswer:<br \/>\n9x\u00b2 &#8211; 6x + 1 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 9, b = -6, and c = 1<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{6 \u00b1 \\sqrt{(-6)\u00b2 &#8211; 4 (1) (9)}}{2 (9)}\\)<br \/>\nx = \\(\\frac{6 \u00b1 \\sqrt{0}}{18}\\)<br \/>\nx = \\(\\frac{6 + 0}{18}\\) or x = \\(\\frac{6 &#8211; 0}{18}\\)<br \/>\nx = \\(\\frac{6}{18}\\) or x = \\(\\frac{6}{18}\\)<br \/>\nx = \\(\\frac{1}{3}\\) or x = \\(\\frac{1}{3}\\)<\/p>\n<p>Question 15.<br \/>\n6x<sup>2<\/sup> &#8211; 13x = -6<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42114\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-15.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 15\" width=\"467\" height=\"528\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-15.png 467w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-15-265x300.png 265w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><\/p>\n<p>Question 16.<br \/>\n-3x<sup>2<\/sup> + 6x = 4<br \/>\nAnswer:<br \/>\n-3x\u00b2 + 6x = 4<br \/>\n-3x\u00b2 + 6x &#8211; 4 = 0<br \/>\n3x\u00b2 &#8211; 6x + 4 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 3, b = -6, and c = 4<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{6 \u00b1 \\sqrt{(-6)\u00b2 &#8211; 4 (3) (4)}}{2 (3)}\\)<br \/>\nx = \\(\\frac{6 \u00b1 \\sqrt{-12}}{6}\\)<br \/>\nx = \\(\\frac{6 \u00b1 12i}{6}\\)<br \/>\nx = 1 \u00b1 2i<\/p>\n<p>Question 17.<br \/>\n1 &#8211; 8x = -16x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42115\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-17.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 17\" width=\"443\" height=\"513\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-17.png 443w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-17-259x300.png 259w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><\/p>\n<p>Question 18.<br \/>\nx<sup>2<\/sup> &#8211; 5x + 3 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 5x + 3 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = -5, and c = 3<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{5 \u00b1 \\sqrt{(-5)\u00b2 &#8211; 4 (1) (3)}}{2 (1)}\\)<br \/>\nx = \\(\\frac{5 \u00b1 \\sqrt{13}}{2}\\)<br \/>\nx = \\(\\frac{5 \u00b1 3.6}{2}\\)<br \/>\nx = \\(\\frac{5 + 3.6}{2}\\) or x = \\(\\frac{5 &#8211; 3.6}{2}\\)<br \/>\nx = 4.3 or x = 0.7<\/p>\n<p>Question 19.<br \/>\nx<sup>2<\/sup> + 2x = 9<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42116\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-19.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 19\" width=\"401\" height=\"467\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-19.png 401w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-19-258x300.png 258w\" sizes=\"(max-width: 401px) 100vw, 401px\" \/><\/p>\n<p>Question 20.<br \/>\n5x<sup>2<\/sup> &#8211; 2 = 4x<br \/>\nAnswer:<br \/>\n5x\u00b2 &#8211; 2 = 4x<br \/>\n5x\u00b2 &#8211; 4x &#8211; 2 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 5, b = -4, and c = -2<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{4 \u00b1 \\sqrt{(-4)\u00b2 + 4 (5) (2)}}{2 (5}\\)<br \/>\nx = \\(\\frac{4 \u00b1 \\sqrt{56}}{10}\\)<br \/>\nx = \\(\\frac{4 \u00b1 7.4}{10}\\)<br \/>\nx = \\(\\frac{4 + 7.4}{10}\\) or x = \\(\\frac{4 &#8211; 7.4}{10}\\)<br \/>\nx = 1.14 or x = -0.34<\/p>\n<p>Question 21.<br \/>\n2x<sup>2<\/sup> + 9x + 7 = 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42117\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-21.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 21\" width=\"443\" height=\"534\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-21.png 443w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-21-249x300.png 249w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><\/p>\n<p>Question 22.<br \/>\n8x<sup>2<\/sup> + 8 = 6 &#8211; 9x<br \/>\nAnswer:<br \/>\n8x\u00b2 + 8 = 6 &#8211; 9x<br \/>\n8x\u00b2 + 9x + 8 &#8211; 6 = 0<br \/>\n8x\u00b2 + 9x + 2 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 8, b = 9, and c = 2<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{-9 \u00b1 \\sqrt{(9)\u00b2 &#8211; 4 (8) (2)}}{2 (8)}\\)<br \/>\nx = \\(\\frac{-9 \u00b1 \\sqrt{17}}{16}\\)<br \/>\nx = \\(\\frac{-9 \u00b1 4.1}{16}\\)<br \/>\nx = \\(\\frac{-9 + 4.1}{16}\\) or x = \\(\\frac{-9 &#8211; 4.1}{16}\\)<br \/>\nx = -0.3 or x = -0.8<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA dolphin jumps out of the water, as shown in the diagram. The function h = -16t<sup>2<\/sup> + 26t models the height h (in feet) of the dolphin after t seconds. After how many seconds is the dolphin at a height of 5 feet?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35360\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-3.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 3\" width=\"262\" height=\"172\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42118\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-23.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 23\" width=\"565\" height=\"530\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-23.png 565w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-23-300x281.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe amount of trout y (in tons) caught in a lake from 1995 to 2014 can be modeled by the equation y = -0.08x<sup>2<\/sup> + 1.6x + 10, where x is the number of years since 1995.<br \/>\na. When were about 15 tons of trout caught in the lake?<br \/>\nAnswer:<br \/>\ny = -0.08x\u00b2 + 1.6x + 10<br \/>\ny = 15<br \/>\n15 = -0.08x\u00b2 + 1.6x + 10<br \/>\n-0.08x\u00b2 + 1.6x &#8211; 5 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115237\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-76.png\" alt=\"\" width=\"564\" height=\"387\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-76.png 564w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-76-300x206.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><br \/>\nAfter 4 years, i.e., in 1999, 15 ton of trout were caught in the lake<\/p>\n<p>b. Do you think this model can be used to determine the amounts of trout caught in future years? Explain your reasoning.<br \/>\nAnswer:<br \/>\nYes, we can use this model to determine the amounts of trout caught in future years but the maximum of trout can be caught only in 16 years<\/p>\n<p><strong>In Exercises 25\u201330, determine the number of real solutions of the equation.<\/strong><br \/>\nQuestion 25.<br \/>\nx<sup>2<\/sup> &#8211; 6x + 10 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42119\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-25.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 25\" width=\"550\" height=\"196\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-25.png 550w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-25-300x107.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 26.<br \/>\nx<sup>2<\/sup> &#8211; 5x &#8211; 3 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 5x &#8211; 3 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = -5, and c = -3<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then there will be 2 real solutions<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then there will be one real solution<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then there are no real solutions<br \/>\nb\u00b2 &#8211; 4ac = (-5)\u00b2 &#8211; 4 (1) (-3)<br \/>\n= 25 + 12<br \/>\n= 37<br \/>\nThere will be 2 solutions for the given equation<\/p>\n<p>Question 27.<br \/>\n2x<sup>2<\/sup> &#8211; 12x = -18<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42120\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-27.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 27\" width=\"556\" height=\"242\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-27.png 556w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-27-300x131.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 28.<br \/>\n4x<sup>2<\/sup> = 4x &#8211; 1<br \/>\nAnswer:<br \/>\n4x\u00b2 = 4x &#8211; 1<br \/>\n4x\u00b2 &#8211; 4x + 1 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 4, b = -4, and c = 1<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then there will be 2 real solutions<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then there will be one real solution<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then there are no real solutions<br \/>\nb\u00b2 &#8211; 4ac = (-4)\u00b2 &#8211; 4 (1) (4)<br \/>\n= 16 &#8211; 16<br \/>\n= 0<br \/>\nThere will be only 1 solution for the given equation<\/p>\n<p>Question 29.<br \/>\n&#8211;\\(\\frac{1}{4}\\)x<sup>2<\/sup> + 4x = -2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42121\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-29.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 29\" width=\"567\" height=\"275\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-29.png 567w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-29-300x146.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 30.<br \/>\n-5x<sup>2<\/sup> + 8x = 9<br \/>\nAnswer:<br \/>\n-5x\u00b2 + 8x = 9<br \/>\n-5x\u00b2 + 8x &#8211; 9 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = -5, b = 8, and c = -9<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then there will be 2 real solutions<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then there will be one real solution<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then there are no real solutions<br \/>\nb\u00b2 &#8211; 4ac = 8\u00b2 &#8211; 4 (-5) (-9)<br \/>\n= 64 &#8211; 180<br \/>\n= -116<br \/>\nThere will be no\u00a0 real solutions for the given equation<\/p>\n<p><strong>In Exercises 31\u201336, find the number of x-intercepts of the graph of the function.<\/strong><br \/>\nQuestion 31.<br \/>\ny = x<sup>2<\/sup> + 5x &#8211; 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42122\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-31.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 31\" width=\"522\" height=\"223\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-31.png 522w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-31-300x128.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/p>\n<p>Question 32.<br \/>\ny = 4x<sup>2<\/sup> + 4x + 1<br \/>\nAnswer:<br \/>\ny = 4x\u00b2 + 4x + 1<br \/>\n4x\u00b2 + 4x + 1 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 4, b = 4, and c = 1<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then there will be 2 x- intercepts<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then there will be one x-intercept<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then there are no x-intercepts<br \/>\nb\u00b2 &#8211; 4ac = 4\u00b2 &#8211; 4 (1) (4)<br \/>\n= 16 &#8211; 16<br \/>\n= 0<br \/>\nThere will be 1 x-intercept for the given equation<\/p>\n<p>Question 33.<br \/>\ny = -6x<sup>2<\/sup> + 3x &#8211; 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42123\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-33.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 33\" width=\"550\" height=\"223\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-33.png 550w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-33-300x122.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 34.<br \/>\ny = -x<sup>2<\/sup> + 5x + 13<br \/>\nAnswer:<br \/>\ny = -x\u00b2 + 5x + 13<br \/>\n-x\u00b2 + 5x + 13 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = -1, b = 5, and c = 13<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then there will be 2 x- intercepts<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then there will be one x-intercept<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then there are no x-intercepts<br \/>\nb\u00b2 &#8211; 4ac = 5\u00b2 &#8211; 4 (-1) (13)<br \/>\n= 25 + 52<br \/>\n= 77<br \/>\nThere are 2 x-intercepts for the given equation<\/p>\n<p>Question 35.<br \/>\nf(x) = 4x<sup>2<\/sup> + 3x &#8211; 6<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42124\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-35.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 35\" width=\"541\" height=\"225\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-35.png 541w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-35-300x125.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 36.<br \/>\nf(x) = 2x<sup>2<\/sup> + 8x + 8<br \/>\nAnswer:<br \/>\ny = 2x\u00b2 + 8x + 8<br \/>\n2x\u00b2 +8x + 8 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 2, b = 8, and c = 8<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then there will be 2 x- intercepts<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then there will be one x-intercept<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then there are no x-intercepts<br \/>\nb\u00b2 &#8211; 4ac = 8\u00b2 &#8211; 4 (2) (8)<br \/>\n= 64 &#8211; 64<br \/>\n= 0<br \/>\nThere is only 1 x-intercept for the given equation<\/p>\n<p><strong>In Exercises 37\u201344, solve the equation using any method. Explain your choice of method.<\/strong><br \/>\nQuestion 37.<br \/>\n-10x<sup>2<\/sup> + 13x = 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42125\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-37.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 37\" width=\"532\" height=\"670\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-37.png 532w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-37-238x300.png 238w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Question 38.<br \/>\nx<sup>2<\/sup> &#8211; 3x &#8211; 40 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 3x &#8211; 40 = 0<br \/>\nx\u00b2 &#8211; 8x + 5x &#8211; 40 = 0<br \/>\nx (x + 5) &#8211; 8 (x + 5) = 0<br \/>\n(x &#8211; 8) (x + 5) = 0<br \/>\nx &#8211; 8 = 0 or x + 5 = 0<br \/>\nx = 8 or x = -5<\/p>\n<p>Question 39.<br \/>\nx<sup>2<\/sup> + 6x = 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-39.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 39\" width=\"571\" height=\"401\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-39.png 571w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-39-300x211.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 40.<br \/>\n-5x<sup>2<\/sup> = -25<br \/>\nAnswer:<br \/>\n-5x\u00b2 = -25<br \/>\n5x\u00b2 = 25<br \/>\nx\u00b2 = \\(\\frac{25}{5}\\)<br \/>\nx\u00b2 = 5<br \/>\nx\u00b2 = d<br \/>\n\u221ax\u00b2 = \u221a5<br \/>\nx = \u00b1\u221a5<br \/>\nThe solution for the above equation is \u00b1\u221a5<\/p>\n<p>Question 41.<br \/>\nx<sup>2<\/sup> + x &#8211; 12 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42127\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-41.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 41\" width=\"580\" height=\"266\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-41.png 580w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-41-300x138.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 42.<br \/>\nx<sup>2<\/sup> &#8211; 4x + 1 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 4x + 1 = 0<br \/>\nx\u00b2 &#8211; 4x + 4 = -1 + 4<br \/>\n(x &#8211; 2)\u00b2 = 3<br \/>\n\u221a(x &#8211; 2)\u00b2 = \u221a3<br \/>\nx &#8211; 2 = \u2212\u221a3 or x &#8211; 2 = \u221a3<br \/>\nx = -\u221a3 + 2 or x = \u221a3 + 2<\/p>\n<p>Question 43.<br \/>\n4x<sup>2<\/sup> &#8211; x = 17<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42128\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-43.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 43\" width=\"562\" height=\"523\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-43.png 562w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-43-300x279.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 44.<br \/>\nx<sup>2<\/sup> + 6x + 9 = 16<br \/>\nAnswer:<br \/>\nx\u00b2 + 6x + 9 = 16<br \/>\nx\u00b2 + 6x = 16 &#8211; 9<br \/>\nx\u00b2 + 6x = 7<br \/>\nx\u00b2 + 6x + 9 = 7 + 9<br \/>\n(x + 3)\u00b2 = 16<br \/>\n\u221a(x + 3)\u00b2 = \u221a16<br \/>\nx + 3 = \u22124 or x + 3 = 4<br \/>\nx = -4 &#8211; 3 or x = 4 &#8211; 3<br \/>\nx = -7 or x = 1<\/p>\n<p>Question 45.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving the equation 3x<sup>2<\/sup> &#8211; 7x &#8211; 6 = 0 using the Quadratic Formula<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35361\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-4.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 4\" width=\"311\" height=\"147\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-4.png 311w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-4-300x142.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42129\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-45.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 45\" width=\"576\" height=\"411\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-45.png 576w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-45-300x214.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving the equation -2x<sup>2<\/sup> + 9x = 4 using the Quadratic Formula.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35362\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-5.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 5\" width=\"328\" height=\"132\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-5.png 328w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-5-300x121.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nAnswer:<br \/>\n-2x\u00b2 + 9x = 4<br \/>\n-2x\u00b2 + 9x &#8211; 4 = 0<br \/>\n2x\u00b2 &#8211; 9x + 4 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 2, b = -9, and c = 4<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{9 \u00b1 \\sqrt{(-9)\u00b2 &#8211; 4 (2) (4)}}{2 (2}\\)<br \/>\nx = \\(\\frac{9 \u00b1 \\sqrt{49}}{4}\\)<br \/>\nx = \\(\\frac{9 \u00b1 7}{4}\\)<br \/>\nx = \\(\\frac{9 + 7}{4}\\) or x = \\(\\frac{9 &#8211; 7}{4}\\)<br \/>\nx = 4 or x = \\(\\frac{1}{2}\\)<br \/>\nThe solutions of the given equation are 4 and \\(\\frac{1}{2}\\)<\/p>\n<p>Question 47.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA fountain shoots a water arc that can be modeled by the graph of the equation y = -0.006x<sup>2<\/sup> + 1.2x + 10, where x is the horizontal distance (in feet) from the river\u2019s north shore and y is the height (in feet) above the river. Does the water arc reach a height of 50 feet? If so, how far from the north shore is the water arc 50 feet above the water?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35363\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-6.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 6\" width=\"265\" height=\"141\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42130\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-47.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 47\" width=\"568\" height=\"560\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-47.png 568w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-47-300x296.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nBetween the months of April and September, the number y of hours of daylight per day in Seattle, Washington, can be modeled by y = -0.00046x<sup>2<\/sup> + 0.076x + 13, where x is the number of days since April 1.<br \/>\na. Do any of the days between April and September in Seattle have 17 hours of daylight? If so, how many?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115426\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-77.png\" alt=\"\" width=\"511\" height=\"421\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-77.png 511w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-77-300x247.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<p>b. Do any of the days between April and September in Seattle have 14 hours of daylight? If so, how many?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115429\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-78.png\" alt=\"\" width=\"566\" height=\"441\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-78.png 566w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-78-300x234.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 49.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend uses the discriminant of the equation 2x<sup>2<\/sup> &#8211; 5x &#8211; 2 = -11 and determines that the equation has two real solutions. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42131\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-49.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 49\" width=\"553\" height=\"318\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-49.png 553w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-49-300x173.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe frame of the tent shown is defined by a rectangular base and two parabolic arches that connect the opposite corners of the base. The graph of y = -0.18x<sup>2<\/sup> + 1.6x models the height y (in feet) of one of the arches x feet along the diagonal of the base. Can a child who is 4 feet tall walk under one of the arches without having to bend over? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35364\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-7.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 7\" width=\"207\" height=\"98\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115431\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-79.png\" alt=\"\" width=\"343\" height=\"144\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-79.png 343w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-79-300x126.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115432\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-80.png\" alt=\"\" width=\"344\" height=\"115\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-80.png 344w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-80-300x100.png 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/><br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong> In Exercises 51 and 52, use the given area A of the rectangle to find the value of x. Then give the dimensions of the rectangle.<br \/>\nQuestion 51.<br \/>\nA = 91 m<sup>2<\/sup><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35365\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-8.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 8\" width=\"219\" height=\"108\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42132\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-51.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 51.1\" width=\"389\" height=\"596\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-51.1.png 389w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-51.1-196x300.png 196w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42133\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-51.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 51.2\" width=\"578\" height=\"249\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-51.2.png 578w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-51.2-300x129.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 52.<br \/>\nA = 209 ft<sup>2<\/sup><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35366\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-9.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 9\" width=\"227\" height=\"116\" \/><br \/>\nAnswer:<br \/>\nl = 4x &#8211; 5<br \/>\nw = 4x + 3<br \/>\nArea = Length \u00d7 Width<br \/>\n209 = (4x &#8211; 5) (4x + 3)<br \/>\n16x\u00b2 + 12x &#8211; 20x &#8211; 15 = 209<br \/>\n16x\u00b2 &#8211; 8x &#8211; 15 &#8211; 209 = 0<br \/>\n16x\u00b2 &#8211; 8x &#8211; 224 = 0<br \/>\n2x\u00b2 &#8211; x &#8211; 28 = 0<br \/>\n2x\u00b2 &#8211; 8x + 7x &#8211; 28 = 0<br \/>\n2x ( x &#8211; 4) + 7 (x &#8211; 4) = 0<br \/>\n(2x + 7) (x &#8211; 4) = 0<br \/>\n2x + 7 = 0 or x &#8211; 4 = 0<br \/>\n2x = -7 or x = 4<br \/>\nx = &#8211;\\(\\frac{7}{2}\\) or x = 4<br \/>\nThe dimensions of a rectangle won&#8217;t be negative<br \/>\nThe value of x is 4<br \/>\nThe length of rectangle = 4x + 3<br \/>\n= 4 (4) + 3<br \/>\n= 16 + 3 = 19 ft<br \/>\nThe width of the rectangle = 4x &#8211; 5<br \/>\n= 4 (4) &#8211; 5<br \/>\n= 16 &#8211; 5<br \/>\n= 11 ft<br \/>\nThe length of the rectangle is 19 ft<br \/>\nThe width of the rectangle is 11 ft<\/p>\n<p><strong>COMPARING METHODS<\/strong> In Exercises 53 and 54, solve the equation by (a) graphing, (b) factoring, and (c) using the Quadratic Formula. Which method do you prefer? Explain your reasoning.<br \/>\nQuestion 53.<br \/>\nx<sup>2<\/sup> + 4x + 4 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42134\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-53.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 53.1\" width=\"491\" height=\"600\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-53.1.png 491w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-53.1-246x300.png 246w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42135\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-53.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 53.2\" width=\"572\" height=\"416\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-53.2.png 572w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-53.2-300x218.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 54.<br \/>\n3x<sup>2<\/sup> + 11x + 6 = 0<br \/>\nAnswer:<br \/>\n3x\u00b2 + 11x + 6 = 0<br \/>\na) By using graphing method:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115433\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-81.png\" alt=\"\" width=\"482\" height=\"509\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-81.png 482w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-81-284x300.png 284w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><br \/>\nb) By using factoring method:<br \/>\n3x\u00b2 + 11x + 6 = 0<br \/>\n3x\u00b2 + 9x + 2x + 6 = 0<br \/>\n3x (x + 3) + 2 (x + 3) = 0<br \/>\n(3x + 2) (x + 3) = 0<br \/>\n3x + 2 = 0 or x + 3 = 0<br \/>\n3x = -2 or x = -3<br \/>\nx = &#8211;\\(\\frac{2}{3}\\) or x = -3<br \/>\nThe solutions for the given equation are -3 and &#8211;\\(\\frac{2}{3}\\)<br \/>\nc) By using the quadratic formula:<br \/>\n3x\u00b2 + 11x + 6 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 3, b = 11, and c = 6<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{-11 \u00b1 \\sqrt{(11)\u00b2 &#8211; 4 (3) (6)}}{2 (3}\\)<br \/>\nx = \\(\\frac{-11 \u00b1 \\sqrt{49}}{6}\\)<br \/>\nx = \\(\\frac{-11 \u00b1 7}{6}\\)<br \/>\nx = \\(\\frac{-11 + 7}{6}\\) or x = \\(\\frac{-11 &#8211; 7}{6}\\)<br \/>\nx = &#8211;\\(\\frac{2}{3}\\) or x = -3<br \/>\nThe solutions of the given equation are -3 and &#8211;\\(\\frac{2}{3}\\)<br \/>\nWe can find the solutions for the given equation easily by using the factoring method<\/p>\n<p>Question 55.<br \/>\n<strong>REASONING<\/strong><br \/>\nHow many solutions does the equation ax<sup>2<\/sup> + bx + c = 0 have when a and c have different signs? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42136\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-55.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 55\" width=\"597\" height=\"110\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-55.png 597w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-55-300x55.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhen the discriminant is a perfect square, are the solutions of ax<sup>2<\/sup> + bx + c = 0 rational or irrational? (Assume a, b, and c are integers.) Explain your reasoning.<br \/>\nAnswer:<br \/>\nThe discriminant is a perfect square<br \/>\nDiscriminant = b\u00b2 &#8211; 4ac<br \/>\nA perfect square means a number that is greater than zero<br \/>\nb\u00b2 &#8211; 4ac &gt; 0<br \/>\nThe solutions of ax\u00b2 + bx + c = 0 are rational<\/p>\n<p><strong>REASONING<\/strong> In Exercises 57\u201359, give a value of c for which the equation has (a) two solutions, (b) one solution, and (c) no solutions.<br \/>\nQuestion 57.<br \/>\nx<sup>2<\/sup> &#8211; 2x + c = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42137\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-57.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 57.1\" width=\"546\" height=\"615\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-57.1.png 546w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-57.1-266x300.png 266w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42138\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-57.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 57.2\" width=\"573\" height=\"436\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-57.2.png 573w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-57.2-300x228.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 58.<br \/>\nx<sup>2<\/sup> &#8211; 8x + c = 0<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 8x + c = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1 and b = -8<br \/>\nDiscriminant (d) = b\u00b2 &#8211; 4ac<br \/>\nIf d &gt; 0, then the equation has 2 real solutions<br \/>\nIf d = 0, then the equation has one solution<br \/>\nIf d &lt; 0, then the equation has no real solutions<br \/>\na) For two solutions:<br \/>\nb\u00b2 &#8211; 4ac &gt; 0<br \/>\n(-8)\u00b2 &#8211; 4 (1) c &gt; 0<br \/>\n64 &#8211; 4c &gt; 0<br \/>\n64 &gt; 4c<br \/>\n\\(\\frac{64}{4}\\) &gt; c<br \/>\n16 &gt; c<br \/>\nc &lt; 16<br \/>\nb) For one solution:<br \/>\nb\u00b2 &#8211; 4ac = 0<br \/>\n(-8)\u00b2 &#8211; 4 (1) c = 0<br \/>\n64 &#8211; 4c = 0<br \/>\n64 = 4c<br \/>\n\\(\\frac{64}{4}\\) = c<br \/>\nc = 16<br \/>\nc) For no solutions:<br \/>\nb\u00b2 &#8211; 4ac &lt; 0<br \/>\n(-8)\u00b2 &#8211; 4 (1) c &lt; 0<br \/>\n64 &#8211; 4c &lt; 0<br \/>\n64 &lt; 4c<br \/>\n\\(\\frac{64}{4}\\) &lt; c<br \/>\n16 &lt; c<br \/>\nc &gt; 16<\/p>\n<p>Question 59.<br \/>\n4x<sup>2<\/sup> + 12x + c = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42139\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-59.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 59.1\" width=\"556\" height=\"618\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-59.1.png 556w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-59.1-270x300.png 270w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42140\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-59.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 59.2\" width=\"572\" height=\"461\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-59.2.png 572w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-59.2-300x242.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 60.<br \/>\n<strong>REPEATED REASONING<\/strong><br \/>\nYou use the Quadratic Formula to solve an equation.<br \/>\na. You obtain solutions that are integers. Could you have used factoring to solve the equation? Explain your reasoning.<br \/>\nAnswer:<br \/>\nYes, the solutions correspond to zeros. If the solutions are p and q, we can write the equation in the form<br \/>\n(x &#8211; p) (x &#8211; q) = 0<br \/>\nThe equation is factorized with the solutions p and q<br \/>\nExample:<br \/>\nIf\u00a0 the solutions are<br \/>\np = 2 and q = -3, then<br \/>\n(x &#8211; 2) (x + 3) = 0<\/p>\n<p>b. You obtain solutions that are fractions. Could you have used factoring to solve the equation? Explain your reasoning.<br \/>\nAnswer:<br \/>\nYes, the reason is the same as in part (a)<br \/>\nExample:<br \/>\nIf the solutions are p = \\(\\frac{1}{2}[\/altex] and q = &#8211;[latex]\\frac{4}{3}\\)<br \/>\n(2x &#8211; 1) (3x + 4) = 0<\/p>\n<p>c. Make a generalization about quadratic equations with rational solutions.<br \/>\nAnswer:<br \/>\nThe quadratic equations with the rational solutions can be easily solved using the &#8220;factoring&#8221; method of the quadratic equation<\/p>\n<p>Question 61.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe fuel economy y(in miles per gallon) of a car can be modeled by the equation y = -0.013x<sup>2<\/sup> + 1.25x + 5.6, where 5 \u2264 x \u2264 75 and x is the speed (in miles per hour) of the car. Find the speed(s) at which you can travel and have a fuel economy of 32 miles per gallon.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42141\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-61.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 61\" width=\"584\" height=\"588\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-61.png 584w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-61-298x300.png 298w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-61-150x150.png 150w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 62.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe depth d (in feet) of a river can be modeled by the equation d = -0.25t<sup>2<\/sup> + 1.7t + 3.5, where 0 \u2264 t \u2264 7 and t is the time (in hours) after a heavy rain begins. When is the river 6 feet deep?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115444\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-83.png\" alt=\"\" width=\"626\" height=\"415\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-83.png 626w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-83-300x199.png 300w\" sizes=\"(max-width: 626px) 100vw, 626px\" \/><\/p>\n<p><strong>ANALYZING EQUATIONS<\/strong> In Exercises 63\u201368, tell whether the vertex of the graph of the function lies above, below, or on the x-axis. Explain your reasoning without using a graph.<br \/>\nQuestion 63.<br \/>\ny = x<sup>2<\/sup> &#8211; 3x + 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42142\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-63.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 63\" width=\"565\" height=\"249\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-63.png 565w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-63-300x132.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 64.<br \/>\ny = 3x<sup>2<\/sup> &#8211; 6x + 3<br \/>\nAnswer:<br \/>\ny = 3x\u00b2 &#8211; 6x + 3<br \/>\n3x\u00b2 &#8211; 6x + 3 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 3, b = -6, and c = 3<br \/>\nb\u00b2 &#8211; 4ac = (-6)\u00b2 &#8211; 4 (3) (3)<br \/>\n= 36 &#8211; 36<br \/>\n= 0<br \/>\nThe discriminant is equal to 0<br \/>\nThe vertex of the given function lies on x-axis<\/p>\n<p>Question 65.<br \/>\ny = 6x<sup>2<\/sup> &#8211; 2x + 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42143\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-65.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 65\" width=\"566\" height=\"251\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-65.png 566w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-65-300x133.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 66.<br \/>\ny = -15x<sup>2<\/sup> + 10x &#8211; 25<br \/>\nAnswer:<br \/>\ny = -15x\u00b2 + 10x &#8211; 25<br \/>\n-15x\u00b2 + 10x &#8211; 25 = 0<br \/>\n15x\u00b2 &#8211; 10x + 25 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 15, b = -10, and c = 25<br \/>\nb\u00b2 &#8211; 4ac = (-10)\u00b2 &#8211; 4 (15) (25)<br \/>\n= 100 &#8211; 1,500<br \/>\n= -1,400<br \/>\nThe discriminant is less than 0<br \/>\nThe graph of y has no x-intercepts and also because a &gt; 0, the graph opens up and has a minimum value.<br \/>\nThe vertex of the graph lies above the x-axis<\/p>\n<p>Question 67.<br \/>\nf(x) = -3x<sup>2<\/sup> &#8211; 4x + 8<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42144\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-67.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 67\" width=\"562\" height=\"249\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-67.png 562w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-67-300x133.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 68.<br \/>\nf(x) = 9x<sup>2<\/sup> &#8211; 24x + 16<br \/>\nAnswer:<br \/>\nf (x) = 9x\u00b2 &#8211; 24x + 16<br \/>\n9x\u00b2 &#8211; 24x + 16 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 9, b = -24, and c = 16<br \/>\nb\u00b2 &#8211; 4ac = (-24)\u00b2 &#8211; 4 (9) (16)<br \/>\n= 576 &#8211; 576<br \/>\n= 0<br \/>\nThe discriminant is equal to 0<br \/>\nThe vertex of the given function lies on the x-axis<\/p>\n<p>Question 69.<br \/>\n<strong>REASONING<\/strong><br \/>\nNASA creates a weightless environment by flying a plane in a series of parabolic paths. The height h (in feet) of a plane after t seconds in a parabolic flight path can be modeled by h = -11t<sup>2<\/sup> + 700t + 21,000. The passengers experience a weightless environment when the height of the plane is greater than or equal to 30,800 feet. For approximately how many seconds do passengers experience weightlessness on such a flight? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35367\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-10.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 10\" width=\"254\" height=\"173\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42145\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-69.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 69\" width=\"553\" height=\"611\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-69.png 553w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-69-272x300.png 272w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 70.<br \/>\n<strong>WRITING EQUATIONS<\/strong><br \/>\nUse the numbers to create a quadratic equation with the solutions x = -1 and x = &#8211;\\(\\frac{1}{4}\\)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35368\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-11.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 11\" width=\"297\" height=\"121\" \/><br \/>\nAnswer:<br \/>\nx = -1 and x = &#8211;\\(\\frac{1}{4}\\)<br \/>\nThe representation of the equation with the solutions are:<br \/>\n(x &#8211; p) (x &#8211; q) = 0(x + 1) (x + \\(\\frac{1}{4}\\)) = 0<br \/>\n(x + 1) (4x + 1) = 0<br \/>\n4x\u00b2 + x + 4x + 1 = 0<br \/>\n4x\u00b2 + 5x + 1 = 0<br \/>\nThe missing numbers of the given equation are: 4, 5, and 1<\/p>\n<p>Question 71.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA rancher constructs two rectangular horse pastures that share a side, as shown. The pastures are enclosed by 1050 feet of fencing. Each pasture has an area of 15,000 square feet.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35369\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-12.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 12\" width=\"318\" height=\"147\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-12.png 318w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-12-300x139.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><br \/>\na. Show that y = 350 &#8211; \\(\\frac{4}{3}\\)x.<br \/>\nb. Find the possible lengths and widths of each pasture.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42146\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-71.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 71.1\" width=\"499\" height=\"619\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-71.1.png 499w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-71.1-242x300.png 242w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42147\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-71.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 71.2\" width=\"531\" height=\"612\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-71.2.png 531w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-71.2-260x300.png 260w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 72.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA kicker punts a football from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35370\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-13.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 13\" width=\"296\" height=\"108\" \/><br \/>\na. Write an equation that models this situation using the function h = -16t<sup>2<\/sup> + v<sup>0<\/sup>t + s<sup>0<\/sup>, where h is the height (in feet) of the football, t is the time (in seconds) after the football is punted, v0 is the initial vertical velocity (in feet per second), and s0 is the initial height (in feet).<br \/>\nb. The football is caught 5.5 feet above the ground, as shown in the diagram. Find the amount of time that the football is in the air.<br \/>\nAnswer:<\/p>\n<p>Question 73.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe solutions of the quadratic equation ax<sup>2<\/sup> + bx + c = 0 are x = \\(\\frac{-b+\\sqrt{b^{2}-4 a c}}{2 a}\\) and x = \\(\\frac{-b-\\sqrt{b^{2}-4 a c}}{2 a}\\). Find the mean of the solutions. How is the mean of the solutions related to the graph of y = ax<sup>2<\/sup> + bx + c? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42148\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-73.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 73\" width=\"579\" height=\"447\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-73.png 579w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-73-300x232.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 74.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nMatch each graph with its discriminant. Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35371\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-14.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 14\" width=\"202\" height=\"464\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-14.png 202w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-14-131x300.png 131w\" sizes=\"(max-width: 202px) 100vw, 202px\" \/><br \/>\na. b<sup>2<\/sup> &#8211; 4ac &gt; 0<br \/>\nAnswer:<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then the quadratic equation will have 2 real roots<br \/>\nWhen we observe the graphs, graph C matches the b\u00b2 &#8211; 4ac &gt; 0<br \/>\nSince a &lt; 0, the quadratic equation will have the parabola closed down and have the maximum value<br \/>\nThe graph of b\u00b2 &#8211; 4ac &gt; 0 will have the maximum value<\/p>\n<p>b. b<sup>2<\/sup> &#8211; 4ac = 0<br \/>\nAnswer:<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then the quadratic equation will have 1 real root<br \/>\nWhen we observe the graphs, graph A matches the b\u00b2 &#8211; 4ac = 0<br \/>\nSince a &lt; 0, the quadratic equation will have the parabola closed down and have the maximum value<br \/>\nThe graph of b\u00b2 &#8211; 4ac = 0 will have the maximum value<\/p>\n<p>c. b<sup>2<\/sup> &#8211; 4ac &lt; 0<br \/>\nAnswer:<br \/>\nIf b\u00b2 &#8211; 4ac&lt; 0, then the quadratic equation will have no real roots<br \/>\nWhen we observe the graphs, graph B matches the b\u00b2 &#8211; 4ac &lt; 0<br \/>\nSince a &gt; 0, the quadratic equation will have the parabola opens up and have the minimum imaginary value<br \/>\nThe graph of b\u00b2 &#8211; 4ac &lt; 0 will have the minimum imaginary value<\/p>\n<p>Question 75.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nYou are trying to hang a tire swing. To get the rope over a tree branch that is 15 feet high, you tie the rope to a weight and throw it over the branch. You release the weight at a height s<sub>0<\/sub> of 5.5 feet. What is the minimum initial vertical velocity v<sub>0<\/sub> needed to reach the branch? (Hint: Use the equation h = -16t<sup>2<\/sup> + v<sub>0<\/sub> t + s<sub>0<\/sub>)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42149\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-75.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 75\" width=\"575\" height=\"540\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-75.png 575w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-75-300x282.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 76.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nConsider the graph of the standard form of a quadratic function y = ax<sup>2<\/sup> + bx + c. Then consider the Quadratic Formula as given by<br \/>\nx = \\(-\\frac{b}{2 a} \\pm \\frac{\\sqrt{b^{2}-4 a c}}{2 a}\\)<br \/>\nWrite a graphical interpretation of the two parts of this formula.<br \/>\nAnswer:<\/p>\n<p>Question 77.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nFind the sum and product of \\(\\frac{-b+\\sqrt{b^{2}-4 a c}}{2 a}\\) and \\(\\frac{-b-\\sqrt{b^{2}-4 a c}}{2 a}\\). Then write a quadratic equation whose solutions have a sum of 2 and a product of \\(\\frac{1}{2}\\).<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42150\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-77.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 77.1\" width=\"415\" height=\"592\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-77.1.png 415w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-77.1-210x300.png 210w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42151\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-77.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 77.2\" width=\"536\" height=\"258\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-77.2.png 536w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-77.2-300x144.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 78.<br \/>\n<strong>WRITING A FORMULA<\/strong><br \/>\nDerive a formula that can be used to find solutions of equations that have the form ax<sup>2<\/sup> + x + c = 0. Use your formula to solve -2x<sup>2<\/sup> + x + 8 = 0.<br \/>\nAnswer:<br \/>\nax\u00b2 + x + c = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = a, b = 1, and c = c<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{-1 \u00b1 \\sqrt{1\u00b2 &#8211; 4 (a) (c)}}{2a}\\)<br \/>\nx = \\(\\frac{-1 \u00b1 \\sqrt{1 &#8211; 4ac}}{2a}\\)<br \/>\nThe solutions of the equation ax\u00b2 + x + c = 0 are: \\(\\frac{-1 \u00b1 \\sqrt{1 &#8211; 4ac}}{2a}\\)<br \/>\n-2x\u00b2 + x + 8 = 0<br \/>\nax\u00b2 + x + c = 0<br \/>\na = -2, b = 1, and c = 8<br \/>\nThe solutions of the above equation are:<br \/>\nx = \\(\\frac{-1 \u00b1 \\sqrt{1 &#8211; 4 (-2) (8)}}{2 (-2)}\\)<br \/>\nx = \\(\\frac{-1 \u00b1 \\sqrt{1 + 64}}{-4}\\)<br \/>\nx = \\(\\frac{-1 \u00b1 \\sqrt{65}}{-4}\\)<br \/>\nx = \\(\\frac{-1 + \\sqrt{65}}{-4}\\) or x = \\(\\frac{-1 &#8211; \\sqrt{65}}{-4}\\)<br \/>\nx = -1.76 or x = 2.26<\/p>\n<p>Question 79.<br \/>\n<strong>MULTIPLE REPRESENTATIONS<\/strong><br \/>\nIf p is a solution of a quadratic equation ax<sup>2<\/sup> + bx + c = 0, then (x &#8211; p) is a factor of ax\u00b2 + bx + c.<br \/>\na. Copy and complete the table for each pair of solutions.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35372\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-15.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 15\" width=\"362\" height=\"145\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-15.png 362w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-15-300x120.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><br \/>\nb. Graph the related function for each equation. Identify the zeros of the function.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42152\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 79.1\" width=\"473\" height=\"473\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.1.png 473w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.1-300x300.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.1-150x150.png 150w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42153\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 79.2\" width=\"362\" height=\"510\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.2.png 362w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.2-213x300.png 213w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42154\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.3.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 79.3\" width=\"342\" height=\"255\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.3.png 342w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.3-300x224.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/p>\n<p><strong>CRITICAL THINKING<\/strong> In Exercises 80\u201382, find all values of k for which the equation has (a) two solutions, (b) one solution, and (c) no solutions.<br \/>\nQuestion 80.<br \/>\n2x<sup>2<\/sup> + x + 3k = 0<br \/>\nAnswer:<br \/>\n2x\u00b2 + x + 3k = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 2, b = 1, and c = 3k<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then the quadratic equation has 2 soltions<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then the quadratic equation has 1 solution<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then the quadratic equation has no real solutions<br \/>\na) For 2 solutions:<br \/>\nb\u00b2 &#8211; 4ac &gt; 0<br \/>\n1\u00b2 &#8211; 4 (2) (3k) &gt; 0<br \/>\n1 &#8211; 24k &gt; 0<br \/>\n1 &gt; 24k<br \/>\n24k &lt; 1<br \/>\nk &lt; \\(\\frac{1}{24}\\)<br \/>\nb) For 1 solution:<br \/>\nb\u00b2 &#8211; 4ac = 0<br \/>\n1\u00b2 &#8211; 4 (2) (3k) = 0<br \/>\n1 &#8211; 24k = 0<br \/>\n1 = 24k<br \/>\n24k = 1<br \/>\nk = \\(\\frac{1}{24}\\)<br \/>\nc) For no solutions:<br \/>\nb\u00b2 &#8211; 4ac &lt; 0<br \/>\n1\u00b2 &#8211; 4 (2) (3k) &lt; 0<br \/>\n1 &#8211; 24k &lt; 0<br \/>\n1 &lt; 24k<br \/>\n24k &gt; 1<br \/>\nk &gt; \\(\\frac{1}{24}\\)<\/p>\n<p>Question 81.<br \/>\nx<sup>2<\/sup> = 4kx + 36 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42155\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-81.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 81.1\" width=\"553\" height=\"607\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-81.1.png 553w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-81.1-273x300.png 273w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42156\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-81.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 81.2\" width=\"558\" height=\"631\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-81.2.png 558w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-81.2-265x300.png 265w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 82.<br \/>\nkx<sup>2<\/sup> + 5x &#8211; 16 = 0<br \/>\nAnswer:<br \/>\nkx\u00b2 + 5x &#8211; 16 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = k, b = 5, and c = -16<br \/>\nIf b\u00b2 &#8211; 4ac &gt; 0, then the quadratic equation has 2 solutions<br \/>\nIf b\u00b2 &#8211; 4ac = 0, then the quadratic equation has 1 solution<br \/>\nIf b\u00b2 &#8211; 4ac &lt; 0, then the quadratic equation has no real solutions<br \/>\na) For 2 solutions:<br \/>\nb\u00b2 &#8211; 4ac &gt; 0<br \/>\n5\u00b2 &#8211; 4 (k) (-16) &gt; 0<br \/>\n25 + 64k &gt; 0<br \/>\n25 &gt; -64k<br \/>\n-64k &lt; 25<br \/>\nk &lt; &#8211;\\(\\frac{25}{64}\\)<br \/>\nb) For 1 solution:<br \/>\nb\u00b2 &#8211; 4ac = 0<br \/>\n5\u00b2 &#8211; 4 (k) (-16) = 0<br \/>\n25 + 64k = 0<br \/>\n25 = -64k<br \/>\n-64k = 25<br \/>\nk = &#8211;\\(\\frac{25}{64}\\)<br \/>\nc) For no solutions:<br \/>\nb\u00b2 &#8211; 4ac &lt; 0<br \/>\n5\u00b2 &#8211; 4 (k) (-16) &lt; 0<br \/>\n25 + 64k = 0<br \/>\n25 &lt; -64k<br \/>\n-64k &gt; 25<br \/>\nk &gt; &#8211;\\(\\frac{25}{64}\\)<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p>Solve the system of linear equations using any method. Explain why you chose the method.<br \/>\nQuestion 83.<br \/>\ny = -x + 4<br \/>\ny = 2x &#8211; 8<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42157\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-83.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 83\" width=\"562\" height=\"574\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-83.png 562w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-83-294x300.png 294w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 84.<br \/>\nx = 16 &#8211; 4y<br \/>\n3x + 4y = 8<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115489\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-84.png\" alt=\"\" width=\"573\" height=\"749\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-84.png 573w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-84-230x300.png 230w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><br \/>\nThe solution of the given system of linear equations is (-4, 5)<\/p>\n<p>Question 85.<br \/>\n2x &#8211; y = 7<br \/>\n2x + 7y = 31<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42158\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-85.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 85\" width=\"531\" height=\"550\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-85.png 531w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-85-290x300.png 290w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 86.<br \/>\n3x &#8211; 2y = -20<br \/>\nx + 1.2y = 6.4<br \/>\nAnswer:<br \/>\n3x &#8211; 2y = -20 &#8212;-(1)<br \/>\nx + 1.2y = 6.4 &#8212;(2)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115490\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-85.png\" alt=\"\" width=\"719\" height=\"987\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-85.png 719w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-85-219x300.png 219w\" sizes=\"(max-width: 719px) 100vw, 719px\" \/><br \/>\nThe solution for the given system of linear equations is: (-2, 7)<\/p>\n<h3><a id=\"Lesson_9.6_Solving_Nonlinear_Systems_of_Equations\"><\/a>Lesson 9.6 Solving Nonlinear Systems of Equations<\/h3>\n<p><strong>Essential Question: <\/strong>How can you solve a system of two equations when one is linear and the other is quadratic?<br \/>\nAnswer:<br \/>\nStep 1: Isolate one of the two variables in one of the equations<br \/>\nStep 2: Substitute the expression that is equal to the isolated variable from step 1 into the other equation<br \/>\nStep 3: Solve the resulting quadratic equation to find the x value(s) of the solution(s)<\/p>\n<p><strong>EXPLORATION 1<\/strong><br \/>\nSolving a System of Equations<br \/>\nWork with a partner. Solve the system of equations by graphing each equation and finding the points of intersection.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35374\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 1\" width=\"222\" height=\"191\" \/><br \/>\nSystem of Equations<br \/>\ny = x + 2<br \/>\ny = x<sup>2<\/sup> + 2x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115500\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-86.png\" alt=\"\" width=\"490\" height=\"498\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-86.png 490w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-86-295x300.png 295w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nThe intersection point of the given system of equations is (1, 3)<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Analyzing Systems of Equations<br \/>\nWork with a partner. Match each system of equations with its graph. Then solve the system of equations.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35375\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 2\" width=\"486\" height=\"369\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-2.png 486w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-2-300x228.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><br \/>\nAnswer:<br \/>\na.<br \/>\ny = x\u00b2 &#8211; 4<br \/>\ny = -x &#8211; 2<br \/>\nx\u00b2 &#8211; 4 = -x &#8211; 2<br \/>\n(x &#8211; 2) (x + 2) = -(x + 2)<br \/>\nx &#8211; 2 = -1<br \/>\nx = -1 + 2<br \/>\nx = 1<br \/>\nFor x = 1,<br \/>\ny = -1 &#8211; 2<br \/>\ny = -3<br \/>\nThe solution or intersection point of the given system of equations is (1, -3)<br \/>\nGraph A matches the solution of the given system of equations<\/p>\n<p>b.<br \/>\ny = x\u00b2 &#8211; 2x + 2<br \/>\ny = 2x &#8211; 2<br \/>\nx\u00b2 &#8211; 2x + 2 = 2x &#8211; 2<br \/>\nx\u00b2 &#8211; 2x &#8211; 2x + 2 + 2 = 0<br \/>\nx\u00b2 &#8211; 4x + 4 = 0<br \/>\n(x &#8211; 2)\u00b2 = 0<br \/>\n\u221ax &#8211; 2 = \u221a0<br \/>\nx &#8211; 2 = 0<br \/>\nx = 2<br \/>\nFor x = 2,<br \/>\ny = 2 (2) &#8211; 2<br \/>\n= 4 &#8211; 2<br \/>\n= 2<br \/>\nThe solution or intersection point of the given system of equations is (2, 2)<br \/>\nGraph C matches the solution of the given system of equations<\/p>\n<p>c.<br \/>\ny = x\u00b2 + 1<br \/>\ny = x &#8211; 1<br \/>\nx\u00b2 + 1 = x &#8211; 1<br \/>\nx\u00b2 &#8211; x + 1 + 1 = 0<br \/>\nx\u00b2- x + 2 = 0<br \/>\nThere will be no solution or intersection point for the given system of equations<br \/>\nGraph B matches the solution of the given system of equations<\/p>\n<p>d.<br \/>\ny = x\u00b2 &#8211; x &#8211; 6<br \/>\ny = 2x &#8211; 2<br \/>\nx\u00b2 &#8211; x &#8211; 6 = 2x &#8211; 2<br \/>\nx\u00b2 &#8211; x &#8211; 2x &#8211; 6 + 2= 0<br \/>\nx\u00b2 &#8211; 3x &#8211; 4 = 0<br \/>\nx\u00b2 &#8211; 4x + x &#8211; 4 = 0<br \/>\nx (x &#8211; 4) + 1 ( x &#8211; 4) = 0<br \/>\n(x + 1) (x &#8211; 4) = 0<br \/>\nx + 1 = 0 or x &#8211; 4 = 0<br \/>\nx = -1 or x = 4<br \/>\nFor x = -1,<br \/>\ny = 2 (-1) &#8211; 2<br \/>\n= -2 &#8211; 2<br \/>\n= -4<br \/>\nFor x = 4,<br \/>\ny = 2 (4) &#8211; 2<br \/>\n= 8 &#8211; 2<br \/>\n= 6<br \/>\nThe solutions or intersection points of the given system of equations are (-1, -4), and (4, 6)<br \/>\nGraph D matches with the solution of the given system of equations<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you solve a system of two equations when one is linear and the other is quadratic?<br \/>\nAnswer:<br \/>\nStep 1: Isolate one of the two variables in one of the equations<br \/>\nStep 2: Substitute the expression that is equal to the isolated variable from step 1 into the other equation<br \/>\nStep 3: Solve the resulting quadratic equation to find the x value(s) of the solution(s)<\/p>\n<p>Question 4.<br \/>\nWrite a system of equations (one linear and one quadratic) that has (a) no solutions, (b) one solution, and (c) two solutions. Your systems should be different from those in Explorations 1 and 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35376\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 3\" width=\"222\" height=\"151\" \/><br \/>\nAnswer:<br \/>\nThe system of equations (one linear and one quadratic) has<br \/>\na) No solutions:<br \/>\ny = x\u00b2 &#8211; 5x + 7<br \/>\ny = x &#8211; 3<\/p>\n<p>b) One solution:<br \/>\ny = x\u00b2 &#8211; 12x + 36<br \/>\ny = x + 7<\/p>\n<p>c) Two solutions:<br \/>\ny = 3x\u00b2 + 11x + 6<br \/>\ny = x + 10<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the system by graphing.<\/strong><br \/>\nQuestion 1.<br \/>\ny = x<sup>2<\/sup> + 4x &#8211; 4<br \/>\ny = 2x &#8211; 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115502\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-87.png\" alt=\"\" width=\"488\" height=\"507\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-87.png 488w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-87-289x300.png 289w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><br \/>\nThe intersection point of the given system of equations is (-6,-6)<\/p>\n<p>Question 2.<br \/>\ny = -x + 6<br \/>\ny = -2x<sup>2<\/sup> &#8211; x + 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115503\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-88.png\" alt=\"\" width=\"488\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-88.png 488w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-88-290x300.png 290w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><\/p>\n<p>There is no intersection point of the 2 equations<\/p>\n<p>Question 3.<br \/>\ny = 3x &#8211; 15<br \/>\ny = \\(\\frac{1}{2}\\)x<sup>2<\/sup> &#8211; 2x &#8211; 7<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115504\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-89.png\" alt=\"\" width=\"496\" height=\"522\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-89.png 496w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-89-285x300.png 285w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><\/p>\n<p>The intersection points of the given system of equations are (8, 9) and (2, -9)<\/p>\n<p><strong>Solve the system by substitution.<\/strong><br \/>\nQuestion 4.<br \/>\ny = x<sup>2<\/sup> + 9 5.<br \/>\ny = 9<br \/>\nAnswer:<br \/>\ny = x\u00b2 + 9.5<br \/>\ny = 9<br \/>\nx\u00b2 + 9.5 = 9<br \/>\nx\u00b2 = 9 &#8211; 9.5<br \/>\nx\u00b2 = -0.5<br \/>\nThe given system of equations has no real solutions<\/p>\n<p>Question 5.<br \/>\ny = -5x<br \/>\ny = x<sup>2<\/sup> &#8211; 3x &#8211; 3<br \/>\nAnswer:<br \/>\ny = -5x<br \/>\ny = x\u00b2 &#8211; 3x &#8211; 3<br \/>\n-5x = x\u00b2 &#8211; 3x &#8211; 3<br \/>\nx\u00b2 &#8211; 3x + 5x &#8211; 3 = 0<br \/>\nx\u00b2 + 2x &#8211; 3 = 0<br \/>\nx\u00b2 + 3x &#8211; x &#8211; 3 = 0<br \/>\nx (x + 3) &#8211; 1 ( x+ 3) = 0<br \/>\n(x &#8211; 1) (x + 3) = 0<br \/>\nx &#8211; 1 = 0 or x + 3 = 0<br \/>\nx = 1 or x = -3<br \/>\nFor x = 1,<br \/>\ny = -5 (1)<br \/>\n= -5<br \/>\nFor x = -3,<br \/>\ny = -5(-3)<br \/>\n= 15<br \/>\nThe intersection points of the given system of equations are (1, -5) and (-3, 15)<\/p>\n<p>Question 6.<br \/>\ny = -3x<sup>2<\/sup> + 2x + 1<br \/>\ny = 5 &#8211; 3x<br \/>\nAnswer:<br \/>\ny = -3x\u00b2 + 2x + 1<br \/>\ny = 5 &#8211; 3x<br \/>\n-3x\u00b2 + 2x + 1 = 5 &#8211; 3x<br \/>\n-3x\u00b2 + 2x + 3x + 1 &#8211; 5 = 0<br \/>\n-3x\u00b2 + 5x &#8211; 4 = 0<br \/>\n3x\u00b2 &#8211; 5x + 4 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 3, b = -5, and c = 4<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{5 \u00b1 \\sqrt{(-5)\u00b2 &#8211; 4 (3) (4)}}{2(3)}\\)<br \/>\nx = \\(\\frac{5 \u00b1 \\sqrt{-23}}{6}\\)<br \/>\nThe given system of equations has no real solutions<\/p>\n<p><strong>Solve the system by elimination.<\/strong><br \/>\nQuestion 7.<br \/>\ny = x<sup>2<\/sup> + x<br \/>\ny = x + 5<br \/>\nAnswer:<br \/>\ny = x\u00b2 + x &#8212;&#8211;(1)<br \/>\ny = x + 5 &#8212;&#8212;(2)<br \/>\neq (1) &#8211; eq (2)<br \/>\ny &#8211; y = x\u00b2 + x &#8211; x &#8211; 5<br \/>\n0 = x\u00b2 &#8211; 5<br \/>\nx\u00b2 = 5<br \/>\n\u221ax\u00b2 = \u221a5<br \/>\nx = \u00b1\u221a5<br \/>\nFor x = \u00b1\u221a5,<br \/>\ny = \u00b1\u221a5 + 5<br \/>\nThe solutions for the given system of equations are: (\u00b1\u221a5, \u00b1\u221a5 + 5)<\/p>\n<p>Question 8.<br \/>\ny = 9x<sup>2<\/sup> + 8x &#8211; 6<br \/>\ny = 5x &#8211; 4<br \/>\nAnswer:<br \/>\ny = 9x\u00b2 + 8x &#8211; 6 &#8212;&#8211;(1)<br \/>\ny = 5x &#8211; 6 &#8212;&#8211;(2)<br \/>\neq (1) &#8211; eq (2)<br \/>\ny &#8211; y = 9x\u00b2 + 8x &#8211; 6 &#8211; 5x + 4<br \/>\n0 = 9x\u00b2+ 3x &#8211; 2<br \/>\n9x\u00b2 + 3x &#8211; 2 = 0<br \/>\n9x\u00b2 + 6x &#8211; 3x &#8211; 2 = 0<br \/>\n3x(3x &#8211; 1) + 2 (3x &#8211; 1) = 0<br \/>\n(3x + 2) (3x &#8211; 1) = 0<br \/>\n3x + 2 = 0 or 3x &#8211; 1 = 0<br \/>\n3x = -2 or 3x = 1<br \/>\nx = &#8211;\\(\\frac{2}{3}\\) or x = \\(\\frac{1}{3}\\)<br \/>\nFor x = &#8211;\\(\\frac{2}{3}\\),<br \/>\ny = 5 (-\\(\\frac{2}{3}\\)) &#8211; 4<br \/>\ny = &#8211;\\(\\frac{22}{3}\\)<br \/>\nFor x = \\(\\frac{1}{3}\\),<br \/>\nx = 5 (\\(\\frac{1}{3}\\)) &#8211; 4<br \/>\nx = &#8211;\\(\\frac{7}{3}\\)<\/p>\n<p><span style=\"font-size: 16px;\">Question 9.<br \/>\n<\/span>y = 2x + 5<br \/>\ny = -3x<sup>2<\/sup> + x &#8211; 4<br \/>\nAnswer:<br \/>\ny = 2x + 5 &#8212;-(1)<br \/>\ny = -3x\u00b2 + x &#8211; 4 &#8212;&#8211;(2)<br \/>\neq (1) &#8211; eq (2)<br \/>\ny &#8211; y = 2x + 5 + 3x\u00b2 &#8211; x + 4<br \/>\n0 = 3x\u00b2 + x + 9<br \/>\n3x\u00b2 + x + 9 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 3, b = 1, and c = 9<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{-1 \u00b1 \\sqrt{(1)\u00b2 &#8211; 4 (3) (9)}}{2(3)}\\)<br \/>\nx = \\(\\frac{-1 \u00b1 \\sqrt{-107}}{6}\\)<br \/>\nThe given system of equations has no real solutions.<\/p>\n<p><strong>Use the method in Example 4 to approximate the solution(s) of the system to the nearest thousandth.<\/strong><br \/>\nQuestion 10.<br \/>\ny = 4<sup>x<\/sup><br \/>\ny = x<sup>2<\/sup> + x + 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115632\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-94.png\" alt=\"\" width=\"478\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-94.png 478w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-94-285x300.png 285w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><br \/>\nThe solution of the given system of equations lies between -2 and -1<\/p>\n<p>Question 11.<br \/>\ny = 4x<sup>2<\/sup> &#8211; 1<br \/>\ny = -2(3)<sup>x<\/sup> + 4<br \/>\nAnswer:<br \/>\ny = 4x\u00b2 &#8211; 1<br \/>\ny = -2 (3^x) + 4<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115633\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-95.png\" alt=\"\" width=\"482\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-95.png 482w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-95-287x300.png 287w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><br \/>\nThe solution for the given system of equations lies between 0 and 1<\/p>\n<p>Question 12.<br \/>\ny = x<sup>2<\/sup> + 3x<br \/>\ny = -x<sup>2<\/sup> + x + 10<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115634\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-96.png\" alt=\"\" width=\"482\" height=\"501\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-96.png 482w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-96-289x300.png 289w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><br \/>\nThe solution for the given system of equations lies between -3 and -2.5<\/p>\n<p><strong>Solve the equation. Round your solution(s) to the nearest hundredth.<\/strong><br \/>\nQuestion 13.<br \/>\n3<sup>x<\/sup> &#8211; 1 = x<sup>2<\/sup> &#8211; 2x + 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115636\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-97.png\" alt=\"\" width=\"486\" height=\"506\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-97.png 486w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-97-288x300.png 288w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><br \/>\nThe solution for the given system of equations lies between 1 and 1.5<\/p>\n<p>Question 14.<br \/>\n4x<sup>2<\/sup> + x = -2 (\\(\\frac{1}{2}\\))<sup>x<\/sup> + 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115637\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-98.png\" alt=\"\" width=\"478\" height=\"534\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-98.png 478w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-98-269x300.png 269w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><br \/>\nThe solution for the given system of equations is (1, 4)<\/p>\n<h3><a id=\"Solving_Nonlinear_Systems_of_Equations_9.6_Exercises\"><\/a>Solving Nonlinear Systems of Equations 9.6 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nDescribe how to use substitution to solve a system of nonlinear equations.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42173\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 1\" width=\"563\" height=\"86\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-1.png 563w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-1-300x46.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow is solving a system of nonlinear equations similar to solving a system of linear equations? How is it different?<br \/>\nAnswer:<br \/>\nIt is similar because you can use the same methods for linear and non-linear equations<br \/>\nHowever, the difference is that sometimes you also need to use different methods and you can obtain multiple solutions<\/p>\n<p><strong>In Exercises 3\u20136, match the system of equations with its graph. Then solve the system.<\/strong><br \/>\nQuestion 3.<br \/>\ny = x<sup>2<\/sup> &#8211; 2x + 1<br \/>\ny = x + 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42174\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 3\" width=\"597\" height=\"543\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-3.png 597w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-3-300x273.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<p>Question 4.<br \/>\ny = x<sup>2<\/sup> + 3x + 2<br \/>\ny = -x &#8211; 3<br \/>\nAnswer:<br \/>\ny = x\u00b2 + 3x + 2<br \/>\ny = -x &#8211; 3<br \/>\nx\u00b2 + 3x + 2 = -x &#8211; 3<br \/>\nx\u00b2 + 3x + 2 + x + 3 = 0<br \/>\nx\u00b2+ 4x + 5 = 0<br \/>\nThere will be no solution or intersection point for the given system of equations<br \/>\nGraph D matches the solution of the given system of equations<\/p>\n<p>Question 5.<br \/>\ny = x &#8211; 1<br \/>\ny = -x<sup>2<\/sup> + x &#8211; 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42175\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 5\" width=\"581\" height=\"349\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-5.png 581w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-5-300x180.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 6.<br \/>\ny = -x + 3<br \/>\ny = -x<sup>2<\/sup> &#8211; 2x + 5<br \/>\nAnswer:<br \/>\ny = -x + 3<br \/>\ny = -x\u00b2 &#8211; 2x + 5<br \/>\n-x + 3 = -x\u00b2 &#8211; 2x + 5<br \/>\nx\u00b2 + 2x &#8211; 5 &#8211; x + 3 = 0<br \/>\nx\u00b2 + x &#8211; 2 = 0<br \/>\nx\u00b2 + 2x &#8211; x &#8211; 2 = 0<br \/>\nx (x + 2) &#8211; 1 (x + 2) = 0<br \/>\n(x &#8211; 1) (x + 2) = 0<br \/>\nx &#8211; 1 = 0 or x + 2 = 0<br \/>\nx = 1 or x = -2<br \/>\nFor x = 1,<br \/>\ny = -1 + 3<br \/>\n= 2<br \/>\nFor x = -2,<br \/>\ny = 2 + 3<br \/>\n= 5<br \/>\nThe solutions or the intersection points of the given system of equations are (1, 2), and (-2, 5)<br \/>\nGraph C matches the given system of equations<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35377\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-4.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 4\" width=\"336\" height=\"276\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-4.png 336w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-4-300x246.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/p>\n<p><strong>In Exercises 7\u201312, solve the system by graphing.<\/strong><br \/>\nQuestion 7.<br \/>\ny = 3x<sup>2<\/sup> &#8211; 2x + 1<br \/>\ny = x + 7<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42176\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 7\" width=\"499\" height=\"746\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-7.png 499w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-7-201x300.png 201w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Question 8.<br \/>\ny = x<sup>2<\/sup> + 2x + 5<br \/>\ny = -2x &#8211; 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115531\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-91.png\" alt=\"\" width=\"500\" height=\"509\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-91.png 500w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-91-295x300.png 295w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><br \/>\nThere are no solutions for the given system of equations<\/p>\n<p>Question 9.<br \/>\ny = -2x<sup>2<\/sup> &#8211; 4x<br \/>\ny = 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42177\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 9\" width=\"497\" height=\"515\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-9.png 497w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-9-290x300.png 290w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/p>\n<p>Question 10.<br \/>\ny = \\(\\frac{1}{2}\\)x<sup>2<\/sup> &#8211; 3x + 4<br \/>\ny = x &#8211; 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115532\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-92.png\" alt=\"\" width=\"490\" height=\"533\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-92.png 490w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-92-276x300.png 276w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nThe solution of the given system of equations is (6, 4)<\/p>\n<p>Question 11.<br \/>\ny = \\(\\frac{1}{3}\\) x<sup>2<\/sup> + 2x &#8211; 3<br \/>\ny = 2x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42178\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-11.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 11.1\" width=\"499\" height=\"514\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-11.1.png 499w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-11.1-291x300.png 291w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42179\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-11.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 11.2\" width=\"452\" height=\"250\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-11.2.png 452w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-11.2-300x166.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><\/p>\n<p>Question 12.<br \/>\ny = 4x<sup>2<\/sup> + 5x &#8211; 7<br \/>\ny = -3x + 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115533\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-93.png\" alt=\"\" width=\"481\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-93.png 481w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-93-286x300.png 286w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\nThe solution of the given system of equations is (1, 2)<\/p>\n<p><strong>In Exercises 13\u201318, solve the system by substitution.<\/strong><br \/>\nQuestion 13.<br \/>\ny = x &#8211; 5<br \/>\ny = x<sup>2<\/sup> + 4x &#8211; 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42180\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 13\" width=\"457\" height=\"479\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-13.png 457w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-13-286x300.png 286w\" sizes=\"(max-width: 457px) 100vw, 457px\" \/><\/p>\n<p>Question 14.<br \/>\ny = -3x<sup>2<\/sup><br \/>\ny = 6x + 3<br \/>\nAnswer:<br \/>\ny = -3x\u00b2<br \/>\ny = 6x + 3<br \/>\n-3x\u00b2 = 6x + 3<br \/>\n3x\u00b2 + 6x + 3 = 0<br \/>\n3x\u00b2 + 3x + 3x + 3 = 0<br \/>\n3x (x + 1) + 3 (x + 1) = 0<br \/>\n(3x + 3) (x + 1) = 0<br \/>\n3x + 3 = 0 or x + 1 = 0<br \/>\n3x = -3 or x = -1<br \/>\nx = -1 or x = -1<br \/>\nFor x = -1,<br \/>\ny = 6 (-1) + 3<br \/>\n= -6 + 3<br \/>\n= -3<br \/>\nThe solution of the given system of equations is (-1, -3)<\/p>\n<p>Question 15.<br \/>\ny = -x + 7<br \/>\ny = -x<sup>2<\/sup> &#8211; 2x &#8211; 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42181\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 15\" width=\"587\" height=\"555\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-15.png 587w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-15-300x284.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 16.<br \/>\ny = -x<sup>2<\/sup> + 7<br \/>\ny = 2x + 4<br \/>\nAnswer:<br \/>\ny = -x\u00b2 + 7<br \/>\ny = 2x + 4<br \/>\n-x\u00b2 + 7 = 2x + 4<br \/>\nx\u00b2 &#8211; 7 + 2x + 4 = 0<br \/>\nx\u00b2 + 2x &#8211; 3 = 0<br \/>\nx\u00b2 + 3x &#8211; x &#8211; 3 = 0<br \/>\nx (x + 3) &#8211; 1 (x + 3) = 0<br \/>\n(x &#8211; 1) (x + 3) = 0<br \/>\nx &#8211; 1 = 0 or x + 3 = 0<br \/>\nx = 1 or x = -3<br \/>\nFor x = 1,<br \/>\ny = 2 (1) + 4<br \/>\n= 6<br \/>\nFor x = -3,<br \/>\ny = 2 (-3) + 4<br \/>\n= -2<br \/>\nThe solutions for the given system of equations are (1, 6), and (-3, -2)<\/p>\n<p>Question 17.<br \/>\ny &#8211; 5 = -x<sup>2<\/sup><br \/>\ny = 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42182\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-17.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 17\" width=\"250\" height=\"403\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-17.png 250w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-17-186x300.png 186w\" sizes=\"(max-width: 250px) 100vw, 250px\" \/><\/p>\n<p>Question 18.<br \/>\ny = 2x<sup>2<\/sup> + 3x &#8211; 4<br \/>\ny &#8211; 4x = 2<br \/>\nAnswer:<br \/>\ny = 2x\u00b2 + 3x &#8211; 4<br \/>\ny &#8211; 4x = 2<br \/>\ny = 4x + 2<br \/>\n2x\u00b2 + 3x &#8211; 4 = 4x + 2<br \/>\n2x\u00b2 + 3x &#8211; 4x &#8211; 4 &#8211; 2 = 0<br \/>\n2x\u00b2 &#8211; x &#8211; 6 = 0<br \/>\n2x\u00b2 &#8211; 4x + 3x &#8211; 6 = 0<br \/>\n2x (x &#8211; 2) + 3 (x &#8211; 2) = 0<br \/>\n(2x + 3) (x &#8211; 2) = 0<br \/>\n2x + 3 = 0 or x &#8211; 2 = 0<br \/>\n2x = -3 or x = 2<br \/>\nx = &#8211;\\(\\frac{3}{2}\\) or x = 2<br \/>\nFor x = &#8211;\\(\\frac{3}{2}\\),<br \/>\ny = 4 (-\\(\\frac{3}{2}\\)) + 2<br \/>\n= -4<br \/>\nFor x = 2,<br \/>\ny = 4 (2) + 2<br \/>\n= 10<br \/>\nThe solutions of the given system of equations are (-\\(\\frac{3}{2}\\), -4), and (2, 10)<\/p>\n<p><strong>In Exercises 19\u201326, solve the system by elimination.<\/strong><br \/>\nQuestion 19.<br \/>\ny = x<sup>2<\/sup> &#8211; 5x &#8211; 7<br \/>\ny = -5x + 9<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42183\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-19.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 19\" width=\"442\" height=\"454\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-19.png 442w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-19-292x300.png 292w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<p>Question 20.<br \/>\ny = -3x<sup>2<\/sup> + x + 2<br \/>\ny = x + 4<br \/>\nAnswer:<br \/>\ny = -3x\u00b2 + x + 2 &#8212;- (1)<br \/>\ny = x + 4 &#8212;- (2)<br \/>\neq (1) &#8211; eq (2)<br \/>\n-3x\u00b2 + x + 2 &#8211; x &#8211; 4 = 0<br \/>\n-3x\u00b2 + x &#8211; x = 4 &#8211; 2<br \/>\n-3x\u00b2 = 2<br \/>\n3x\u00b2 = -2<br \/>\nThe given system of equations does not have any real solutions<\/p>\n<p>Question 21.<br \/>\ny = -x<sup>2<\/sup> &#8211; 2x + 2<br \/>\ny = 4x + 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42184\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-21.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 21\" width=\"434\" height=\"474\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-21.png 434w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-21-275x300.png 275w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/p>\n<p>Question 22.<br \/>\ny = -2x<sup>2<\/sup> + x &#8211; 3<br \/>\ny = 2x &#8211; 2<br \/>\nAnswer:<br \/>\ny = -2x\u00b2 + x &#8211; 3 &#8212;-(1)<br \/>\ny = 2x &#8211; 2 &#8212;-(2)<br \/>\neq (1) &#8211; eq (2)<br \/>\nSo,<br \/>\n-2x\u00b2 + x &#8211; 3 &#8211; 2x + 2 = 0<br \/>\n-2x\u00b2 &#8211; x &#8211; 1 = 0<br \/>\n2x\u00b2 + x + 1 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 2, b = 1, and c = 1<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{-1 \u00b1 \\sqrt{1\u00b2 &#8211; 4 (2) (1)}}{2 (2)}\\)<br \/>\nx = \\(\\frac{-1 \u00b1 \\sqrt{-7}}{4}\\)<br \/>\nThe given system of equations does not have any real solutions<\/p>\n<p>Question 23.<br \/>\ny = 2x &#8211; 1<br \/>\ny = x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42185\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-23.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 23\" width=\"331\" height=\"414\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-23.png 331w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-23-240x300.png 240w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><\/p>\n<p>Question 24.<br \/>\ny = x<sup>2<\/sup> + x + 1<br \/>\ny = -x &#8211; 2<br \/>\nAnswer:<br \/>\ny = x\u00b2 + x + 1 &#8212;-(1)<br \/>\ny = -x &#8211; 2 &#8212;-(2)<br \/>\neq (1) &#8211; eq (2)<br \/>\nx\u00b2 + x + 1 + x + 2 = 0<br \/>\nx\u00b2 + 2x + 3 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = 2, and c = 3<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{-2 \u00b1 \\sqrt{2\u00b2 &#8211; 4 (3) (1)}}{2 (1)}\\)<br \/>\nx = \\(\\frac{-2 \u00b1 \\sqrt{-8}}{2}\\)<br \/>\nThe given system of equations does not have any real solutions<\/p>\n<p>Question 25.<br \/>\ny + 2x = 0<br \/>\ny = x<sup>2<\/sup> + 4x &#8211; 6<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42186\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-25.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 25.1\" width=\"327\" height=\"589\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-25.1.png 327w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-25.1-167x300.png 167w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42187\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-25.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 25.2\" width=\"574\" height=\"243\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-25.2.png 574w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-25.2-300x127.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 26.<br \/>\ny = 2x &#8211; 7<br \/>\ny + 5x = x<sup>2<\/sup> &#8211; 2<br \/>\nAnswer:<br \/>\ny = 2x &#8211; 7 &#8212;&#8211; (1)<br \/>\ny = x\u00b2 &#8211; 5x &#8212;&#8211;(2)<br \/>\neq (1) &#8211; eq (2)<br \/>\n2x &#8211; 7 &#8211; x\u00b2 + 5x = 0<br \/>\n-x\u00b2 + 7x &#8211; 7 = 0<br \/>\nx\u00b2 &#8211; 7x + 7 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = -7, and c = 7<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{7 \u00b1 \\sqrt{(-7)\u00b2 &#8211; 4 (7) (1)}}{2 (1)}\\)<br \/>\nx = \\(\\frac{7 \u00b1 \\sqrt{21}}{2}\\)<br \/>\nx = \\(\\frac{7 + \\sqrt{21}}{2}\\) or x = \\(\\frac{7 &#8211; \\sqrt{21}}{2}\\)<br \/>\nx = 5.79 or x = 1.20<br \/>\nThe solutions for the given system of equations are 5.79 and 1.20<\/p>\n<p>Question 27.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving the system of equations by graphing.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35378\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 5\" width=\"326\" height=\"170\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-5.png 326w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-5-300x156.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42188\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-27.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 27\" width=\"395\" height=\"321\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-27.png 395w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-27-300x244.png 300w\" sizes=\"(max-width: 395px) 100vw, 395px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving for one of the variables in the system.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35379\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-6.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 6\" width=\"316\" height=\"136\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-6.png 316w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-6-300x129.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer:<br \/>\ny = 3x\u00b2 &#8211; 6x + 4<br \/>\ny = 4<br \/>\n3x\u00b2 &#8211; 6x + 4 = 4<br \/>\n3x\u00b2- 6x = 4 &#8211; 4<br \/>\n3x\u00b2= 6x<br \/>\n3x = 6<br \/>\nx = \\(\\frac{6}{3}\\)<br \/>\nx = 2<br \/>\nThe solution of the given system of equations is (2, 4)<\/p>\n<p><strong>In Exercises 29\u201332, use the table to describe the locations of the zeros of the quadratic function f.<\/strong><br \/>\nQuestion 29.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35380\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 7\" width=\"299\" height=\"67\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42189\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-29.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 29\" width=\"563\" height=\"164\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-29.png 563w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-29-300x87.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 30.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35381\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-8.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 8\" width=\"296\" height=\"65\" \/><br \/>\nAnswer:<br \/>\nThere is a sign change between x = 1 and x = 2 and f (1) and f (2) are in the same distance,<br \/>\nThe first solution lies between 1 and 2<br \/>\nThere is a sign change between x = 3 and x = 4 and f (3) and f (4) are in the same distance,<br \/>\nThe second solution lies between 3 and 4<br \/>\nThe solutions for the given function will lie between (1, 2) and (3, 4)<\/p>\n<p>Question 31.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35382\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 9\" width=\"299\" height=\"70\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42190\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-31.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 31\" width=\"570\" height=\"167\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-31.png 570w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-31-300x88.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 32.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35383\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-10.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 10\" width=\"291\" height=\"68\" \/><br \/>\nAnswer:<br \/>\nThere is a sign change between x = 2 and x = 3 and f (2) and f (3) are in the same distance,<br \/>\nBut, f (3) is very close to 0<br \/>\nThe first solution is closer to 3 than 2<br \/>\nThere is a sign change between x = 5 and x = 6 and f (5) and f (6) are in the same distance,<br \/>\nBut, f (5) is very close to 0<br \/>\nThe second solution is closer to 5 than 6<br \/>\nThe solution for the given function will lie between (3, 5)<\/p>\n<p><strong>In Exercises 33\u201338, use the method in Example 4 to approximate the solution(s) of the system to the nearest thousandth.<\/strong><br \/>\nQuestion 33.<br \/>\ny = x<sup>2<\/sup> + 2x + 3<br \/>\ny = 3<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42191\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-33.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 33.1\" width=\"446\" height=\"558\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-33.1.png 446w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-33.1-240x300.png 240w\" sizes=\"(max-width: 446px) 100vw, 446px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42192\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-33.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 33.2\" width=\"510\" height=\"245\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-33.2.png 510w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-33.2-300x144.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p>Question 34.<br \/>\ny = 2<sup>x<\/sup> + 5<br \/>\ny = x<sup>2<\/sup> &#8211; 3x + 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115640\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-99.png\" alt=\"\" width=\"488\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-99.png 488w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-99-290x300.png 290w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><br \/>\nThe solution for the given system of equations is approximately (1, 6)<\/p>\n<p>Question 35.<br \/>\ny = 2(4)<sup>x<\/sup> &#8211; 1<br \/>\ny = 3x<sup>2<\/sup> + 8x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42193\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-35.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 35.1\" width=\"609\" height=\"555\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-35.1.png 609w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-35.1-300x273.png 300w\" sizes=\"(max-width: 609px) 100vw, 609px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42194\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-35.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 35.2\" width=\"621\" height=\"724\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-35.2.png 621w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-35.2-257x300.png 257w\" sizes=\"(max-width: 621px) 100vw, 621px\" \/><\/p>\n<p>Question 36.<br \/>\ny = -x<sup>2<\/sup> &#8211; 4x &#8211; 4<br \/>\ny = -5<sup>x<\/sup> &#8211; 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115641\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-100.png\" alt=\"\" width=\"489\" height=\"505\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-100.png 489w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-100-290x300.png 290w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nThe solution for the given system of equations is approximately (-1, -3)<\/p>\n<p>Question 37.<br \/>\ny = -x<sup>2<\/sup> &#8211; x + 5<br \/>\ny = 2x<sup>2<\/sup> + 6x &#8211; 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42195\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-37.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 37.1\" width=\"753\" height=\"606\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-37.1.png 753w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-37.1-300x241.png 300w\" sizes=\"(max-width: 753px) 100vw, 753px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42196\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-37.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 37.2\" width=\"788\" height=\"626\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-37.2.png 788w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-37.2-300x238.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-37.2-768x610.png 768w\" sizes=\"(max-width: 788px) 100vw, 788px\" \/><\/p>\n<p>Question 38.<br \/>\ny = 2x<sup>2<\/sup> + x &#8211; 8<br \/>\ny = x<sup>2<\/sup> &#8211; 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115642\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-101.png\" alt=\"\" width=\"479\" height=\"507\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-101.png 479w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-101-283x300.png 283w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nThe approximate solution for the given system of equations is (-1, 2)<\/p>\n<p><strong>In Exercises 39\u201346, solve the equation. Round your solution(s) to the nearest hundredth.<\/strong><br \/>\nQuestion 39.<br \/>\n3x + 1 = x<sup>2<\/sup> + 7x &#8211; 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42197\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-39.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 39\" width=\"544\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-39.png 544w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-39-300x278.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 40.<br \/>\n-x<sup>2<\/sup> + 2x = -2x + 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115643\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-102.png\" alt=\"\" width=\"485\" height=\"506\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-102.png 485w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-102-288x300.png 288w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nThere are no solutions for the given system of equations<\/p>\n<p>Question 41.<br \/>\nx<sup>2<\/sup> &#8211; 6x + 4 = -x<sup>2<\/sup> &#8211; 2x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42198\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-41.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 41\" width=\"575\" height=\"269\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-41.png 575w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-41-300x140.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 42.<br \/>\n2x<sup>2<\/sup> + 8x + 10 = -x<sup>2<\/sup> &#8211; 2x + 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115645\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-103.png\" alt=\"\" width=\"480\" height=\"507\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-103.png 480w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-103-284x300.png 284w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><br \/>\nThe approximate solution for the given equation is (-1, 6)<\/p>\n<p>Question 43.<br \/>\n-4 (\\(\\frac{1}{2}\\))<sup>x<\/sup> = -x<sup>2<\/sup> &#8211; 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42199\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-43.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 43\" width=\"574\" height=\"307\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-43.png 574w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-43-300x160.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 44.<br \/>\n1.5(2)<sup>x<\/sup> &#8211; 3 = -x<sup>2<\/sup> + 4x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115646\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-104.png\" alt=\"\" width=\"477\" height=\"506\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-104.png 477w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-104-283x300.png 283w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><br \/>\nThe approximate solutions for the given equation are (2, 4) and ((0, -2)<\/p>\n<p>Question 45.<br \/>\n8<sup>x-2<\/sup> + 3 = 2 (\\(\\frac{3}{2}\\))<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42200\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-45.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 45\" width=\"575\" height=\"512\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-45.png 575w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-45-300x267.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 46.<br \/>\n-0.5(4)<sup>x<\/sup> = 5<sup>x<\/sup> &#8211; 6<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115648\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-105.png\" alt=\"\" width=\"478\" height=\"507\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-105.png 478w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-105-283x300.png 283w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><br \/>\nThe solution for the given equation is (1, -2)<\/p>\n<p>Question 47.<br \/>\n<strong>COMPARING METHODS<\/strong><br \/>\nSolve the system in Exercise 37 using substitution. Compare the exact solutions to the approximated solutions.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42201\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-47.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 47.1\" width=\"357\" height=\"628\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-47.1.png 357w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-47.1-171x300.png 171w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42202\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-47.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 47.2\" width=\"528\" height=\"628\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-47.2.png 528w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-47.2-252x300.png 252w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>COMPARING METHODS<\/strong><br \/>\nSolve the system in Exercise 38 using elimination. Compare the exact solutions to the approximated solutions.<br \/>\nAnswer:<br \/>\ny = 2x\u00b2 + x &#8211; 8 &#8212;-(1)<br \/>\ny = x\u00b2 &#8211; 5 &#8212;&#8211;(2)<br \/>\neq (1) &#8211; eq(2)<br \/>\n2x\u00b2 + x &#8211; 8 = x\u00b2 &#8211; 5<br \/>\n2x\u00b2 &#8211; x\u00b2 + x &#8211; 8 + 5 = 0<br \/>\nx\u00b2 + x &#8211; 3 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b= 1, and c = -3<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{-1 \u00b1 \\sqrt{1\u00b2 + 4 (1) (3)}}{2 (1)}\\)<br \/>\nx = \\(\\frac{-1 \u00b1 \\sqrt{13}}{2}\\)<br \/>\nx = \\(\\frac{-1 + \\sqrt{13}}{2}\\) or x = \\(\\frac{-1 &#8211; \\sqrt{13}}{2}\\)<br \/>\nWe know that,<br \/>\n\\(\\sqrt{13}\\) = 3.60<br \/>\nx = 1.30 or x = -2.30<br \/>\nThe exact solutions and approximate solutions are the same<\/p>\n<p>Question 49.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe attendances y for two movies can be modeled by the following equations, where x is the number of days since the movies opened.<br \/>\ny = -x<sup>2<\/sup> + 35x + 100 Movie A<br \/>\ny = -5x + 275 Movie B<br \/>\nWhen is the attendance for each movie the same?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42203\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-49.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 49\" width=\"575\" height=\"334\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-49.png 575w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-49-300x174.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou and a friend are driving boats on the same lake. Your path can be modeled by the equation y = -x<sup>2<\/sup> &#8211; 4x &#8211; 1, and your friend\u2019s path can be modeled by the equation y = -2x + 8. Do your paths cross each other? If so, what are the coordinates of the point(s) where the paths meet?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35384\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 11\" width=\"297\" height=\"138\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115650\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-106.png\" alt=\"\" width=\"478\" height=\"510\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-106.png 478w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-106-281x300.png 281w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><br \/>\nThe paths of yours and your friend did not cross each other<\/p>\n<p>Question 51.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe arch of a bridge can be modeled by y = -0.002x<sup>2<\/sup> + 1.06x, where x is the distance (in meters) from the left pylons and y is the height (in meters) of the arch above the water. The road can be modeled by the equation y = 52. To the nearest meter, how far from the left pylons are the two points where the road intersects the arch of the bridge?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35385\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-12.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 12\" width=\"331\" height=\"159\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-12.png 331w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-12-300x144.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42204\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-51.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 51\" width=\"577\" height=\"598\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-51.png 577w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-51-289x300.png 289w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says that a system of equations consisting of a linear equation and a quadratic equation can have zero, one, two, or infinitely many solutions. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115651\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-107.png\" alt=\"\" width=\"508\" height=\"100\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-107.png 508w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-107-300x59.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/p>\n<p><strong>COMPARING METHODS<\/strong> In Exercises 53 and 54, solve the system of equations by (a) graphing, (b) substitution, and (c) elimination. Which method do you prefer? Explain your reasoning.<br \/>\nQuestion 53.<br \/>\ny = 4x + 3<br \/>\ny = x<sup>2<\/sup> + 4x &#8211; 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42205\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-53.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 53.1\" width=\"506\" height=\"647\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-53.1.png 506w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-53.1-235x300.png 235w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42206\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-53.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 53.2\" width=\"579\" height=\"620\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-53.2.png 579w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-53.2-280x300.png 280w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 54.<br \/>\ny = x<sup>2<\/sup> &#8211; 5<br \/>\ny = -x + 7<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115652\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-108.png\" alt=\"\" width=\"483\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-108.png 483w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-108-288x300.png 288w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><br \/>\nThe solution for the given system of equations is (3, 4)<br \/>\nb) By substitution:<br \/>\nx\u00b2 &#8211; 5 = -x + 7<br \/>\nx\u00b2 + x &#8211; 5 &#8211; 7 = 0<br \/>\nx\u00b2 + x &#8211; 12 = 0<br \/>\nx\u00b2 + 4x &#8211; 3x &#8211; 12 = 0<br \/>\nx (x &#8211; 3) + 4 (x &#8211; 3) = 0<br \/>\n(x + 4) (x &#8211; 3) = 0<br \/>\nx + 4 = 0 or x &#8211; 3 = 0<br \/>\nx = -4 or x = 3<br \/>\nFor x = 3,<br \/>\ny = -3 + 7<br \/>\n= 4<br \/>\nFor x = -4,<br \/>\ny = 4 + 7<br \/>\n= 11<br \/>\nThe solutions for the given system of equations are (3, 4) and (-4, 11)<br \/>\nc) By elimination:<br \/>\nSince the variable on the left side of the given system of equations is equal,<br \/>\neq (1) &#8211; eq (2) = 0<br \/>\nSo,<br \/>\nx\u00b2 + x &#8211; 5 &#8211; 7 = 0<br \/>\nx\u00b2 + x &#8211; 12 = 0<br \/>\nx\u00b2 + 4x &#8211; 3x &#8211; 12 = 0<br \/>\nx (x &#8211; 3) + 4 (x &#8211; 3) = 0<br \/>\n(x + 4) (x &#8211; 3) = 0<br \/>\nx + 4 = 0 or x &#8211; 3 = 0<br \/>\nx = -4 or x = 3<br \/>\nFor x = 3,<br \/>\ny = -3 + 7<br \/>\n= 4<br \/>\nFor x = -4,<br \/>\ny = 4 + 7<br \/>\n= 11<br \/>\nThe solutions for the given system of equations are (3, 4) and (-4, 11)<br \/>\nWe can prefer the substitution method because of the factorization method.<\/p>\n<p>Question 55.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe function y = -x<sup>2<\/sup> + 65x + 256 models the number y of subscribers to a website, where x is the number of days since the website launched. The number of subscribers to a competitor\u2019s website can be modeled by a linear function. The websites have the same number of subscribers on Days 1 and 34.<br \/>\na. Write a linear function that models the number of subscribers to the competitor\u2019s website.<br \/>\nb. Solve the system to verify the function from part (a).<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42207\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-55.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 55.1\" width=\"564\" height=\"613\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-55.1.png 564w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-55.1-276x300.png 276w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42208\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-55.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 55.2\" width=\"586\" height=\"326\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-55.2.png 586w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-55.2-300x167.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe diagram shows the graphs of two equations in a system that has one solution.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35386\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 13\" width=\"195\" height=\"186\" \/><br \/>\na. How many solutions will the system have when you change the linear equation to y = c + 2?<br \/>\nAnswer:<br \/>\nWe can observe that y = c is a constant line that is parallel to the x-axis<br \/>\ny = c + 2 is also a constant line<br \/>\nWe can conclude that the system will have only one solution when you change the linear equation to y = c + 2<\/p>\n<p>b. How many solutions will the system have when you change the linear equation to y = c &#8211; 2?<br \/>\nAnswer:<br \/>\nWe can observe that y = c is a constant line that is parallel to the x-axis<br \/>\ny = c &#8211; 2 is also a constant line<br \/>\nWe can conclude that the system will have only one solution when you change the linear equation to y = c &#8211; 2<\/p>\n<p>Question 57.<br \/>\n<strong>WRITING<\/strong><br \/>\nA system of equations consists of a quadratic equation whose graph opens up and a quadratic equation whose graph opens down. Describe the possible number of solutions of the system. Sketch examples to justify your answer.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42209\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-57.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 57\" width=\"588\" height=\"359\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-57.png 588w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-57-300x183.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 58.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nThe population of a country is 2 million people and increases by 3% each year. The country\u2019s food supply is sufficient to feed 3 million people and increases at a constant rate that feeds 0.25 million additional people each year.<br \/>\na. When will the country first experience a food shortage?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115658\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-109.png\" alt=\"\" width=\"457\" height=\"573\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-109.png 457w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-109-239x300.png 239w\" sizes=\"(max-width: 457px) 100vw, 457px\" \/><\/p>\n<p>b. The country doubles the rate at which its food supply increases. Will food shortages still occur? If so, in what year?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115659\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-110.png\" alt=\"\" width=\"427\" height=\"370\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-110.png 427w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-110-300x260.png 300w\" sizes=\"(max-width: 427px) 100vw, 427px\" \/><\/p>\n<p>Question 59.<br \/>\n<strong>ANALYZING GRAPHS<\/strong><br \/>\nUse the graphs of the linear and quadratic functions.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35387\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-14.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 14\" width=\"245\" height=\"194\" \/><br \/>\na. Find the coordinates of point A.<br \/>\nb. Find the coordinates of point B.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42210\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-59.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 59.1\" width=\"450\" height=\"621\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-59.1.png 450w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-59.1-217x300.png 217w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42211\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-59.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 59.2\" width=\"427\" height=\"276\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-59.2.png 427w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-59.2-300x194.png 300w\" sizes=\"(max-width: 427px) 100vw, 427px\" \/><\/p>\n<p>Question 60.<br \/>\n<strong>THOUGHT-PROVOKING<\/strong><br \/>\nIs it possible for a system of two quadratic equations to have exactly three solutions? exactly four solutions? Explain your reasoning. (Hint: Rotations of the graphs of quadratic equations still represent quadratic equations.)<br \/>\nAnswer:<br \/>\nThe quadratic equation is in the form of<br \/>\nax\u00b2 + bx + c = 0<br \/>\nWe can say that the quadratic equation will have only an even number of solutions even we consider the rotations of the graphs of the quadratic equations<br \/>\nThe quadratic equation will have exactly four solutions<\/p>\n<p>Question 61.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nSolve the system of three equations shown.<br \/>\ny = 2x &#8211; 8<br \/>\ny = x<sup>2<\/sup> &#8211; 4x &#8211; 3<br \/>\ny = -3(2)<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42212\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-61.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 61\" width=\"620\" height=\"366\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-61.png 620w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-61-300x177.png 300w\" sizes=\"(max-width: 620px) 100vw, 620px\" \/><\/p>\n<p>Question 62.<br \/>\n<strong>PROBLEM-SOLVING<\/strong><br \/>\nFind the point(s) of intersection, if any, of the line y = -x &#8211; 1 and the circle x<sup>2<\/sup> + y<sup>2<\/sup> = 41.<br \/>\nAnswer:<br \/>\ny = -x &#8211; 1 &#8212;-\u00a0 (1)<br \/>\nx\u00b2 + y\u00b2 = 41 &#8212;- (2)<br \/>\nSubstitute eq (1) into eq (2)<br \/>\nx\u00b2 + (-x &#8211; 1)\u00b2 = 41<br \/>\nx\u00b2 + x\u00b2 + 1 + 2x = 41<br \/>\n2x\u00b2 + 2x &#8211; 40 = 0<br \/>\nx\u00b2+ x &#8211; 20 = 0<br \/>\nx\u00b2 + 5x &#8211; 4x &#8211; 20 = 0<br \/>\nx ( x + 5 ) &#8211; 4 (x + 5) = 0<br \/>\n(x &#8211; 4) (x + 5) = 0<br \/>\nx &#8211; 4 = 0 or x + 5 = 0<br \/>\nx = 4 or x = -5<br \/>\nFor x = 4,<br \/>\ny = -4 &#8211; 1<br \/>\n= -5<br \/>\nFor x = -5,<br \/>\ny = 5 &#8211; 1,<br \/>\n= 4<br \/>\nThe points of intersection for the given equations are (4, -5) and (-5, 4)<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Graph the system of linear inequalities.<\/strong><br \/>\nQuestion 63.<br \/>\ny &gt; 2x<br \/>\ny &gt; -x + 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42213\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-63.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 63\" width=\"241\" height=\"235\" \/><\/p>\n<p>Question 64.<br \/>\ny \u2265 4x + 1<br \/>\ny \u2264 7<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115661\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-111.png\" alt=\"\" width=\"476\" height=\"496\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-111.png 476w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-111-288x300.png 288w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><\/p>\n<p>Question 65.<br \/>\ny &#8211; 3 \u2264 -2x<br \/>\ny + 5 &lt; 3x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115663\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-112.png\" alt=\"\" width=\"476\" height=\"497\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-112.png 476w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-112-287x300.png 287w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><\/p>\n<p>Question 66.<br \/>\nx + y &gt; -6<br \/>\n2y \u2264 3x + 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42214\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-65.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 65\" width=\"486\" height=\"346\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-65.png 486w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-65-300x214.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p><strong>Graph the function. Describe the domain and range.<\/strong><br \/>\nQuestion 67.<br \/>\ny = 3x<sup>2<\/sup> + 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42215\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-67.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 67\" width=\"467\" height=\"428\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-67.png 467w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-67-300x275.png 300w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><\/p>\n<p>Question 68.<br \/>\ny = -x<sup>2<\/sup> &#8211; 6x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115664\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-113.png\" alt=\"\" width=\"487\" height=\"505\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-113.png 487w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-113-289x300.png 289w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><br \/>\nThe domain is the range of values of x that make the equation positive<br \/>\nThe range is the range of values of y that make the equation positive<br \/>\nThe domain of the given function is: 0 \u2264 x \u2264 -6<br \/>\nThe range of the given function is: -10 \u2264 y \u2264 9<\/p>\n<p>Question 69.<br \/>\ny = -2x<sup>2<\/sup> + 12x &#8211; 7<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-42216\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-69.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 69\" width=\"491\" height=\"423\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-69.png 491w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-69-300x258.png 300w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><\/p>\n<p>Question 70.<br \/>\ny = 5x<sup>2<\/sup> + 10x &#8211; 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115665\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-114.png\" alt=\"\" width=\"485\" height=\"509\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-114.png 485w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-114-286x300.png 286w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nThe domain is the set of all the values of x that make the equation positive<br \/>\nThe range is the set of all the values of y that make the equation positive<br \/>\nThe approximate domain of the given function is: -2 \u2264 x \u2264 0<br \/>\nThe range of the given equation is: -8 \u2264 y \u2264 10<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Performance_Task:_Form_Matters\"><\/a>Solving Quadratic Equations Performance Task: Form Matters<\/h3>\n<p><strong>9.4\u20139.6 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35388\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 15\" width=\"651\" height=\"57\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-15.png 651w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-15-300x26.png 300w\" sizes=\"(max-width: 651px) 100vw, 651px\" \/><\/p>\n<p><strong>Core Concepts<\/strong><br \/>\nSection 9.4<br \/>\nCompleting the Square, p. 506<\/p>\n<p>Section 9.5<br \/>\nQuadratic Formula, p. 516<br \/>\nInterpreting the Discriminant, p. 518<\/p>\n<p>Section 9.6<br \/>\nSolving Systems of Nonlinear Equations, p. 526<\/p>\n<p><strong>Mathematical Practices<\/strong><br \/>\nQuestion 1.<br \/>\nHow does your answer to Exercise 74 on page 514 help create a shortcut when solving some quadratic equations by completing the square?<br \/>\nAnswer:<br \/>\nFor the equation that is of the form<br \/>\nax\u00b2 + bx + c<br \/>\nWhen we use the &#8220;Completing the squares&#8221; method,<br \/>\nc = (\\(\\frac{b}{2}\\))\u00b2 and in place of b,<br \/>\nb = \\(\\frac{b}{2}\\)<\/p>\n<p>Question 2.<br \/>\nWhat logical progression led you to your answer in Exercise 55 on page 522?<br \/>\nAnswer:<br \/>\nIn Exercise 55 on page 522,<br \/>\nWe use the sign changes for a and c and find the discriminant to find the logical procession<\/p>\n<p>Question 3.<br \/>\nCompare the methods used to solve Exercise 53 on page 532. Discuss the similarities and differences among the methods.<br \/>\nAnswer:<\/p>\n<p><strong>Performance Task Form Matters<\/strong><\/p>\n<p>Each form of a quadratic function has its pros and cons. Using one form, you can easily find the vertex, but the zeros are more difficult to find. Using another form, you can easily find the y-intercept, but the vertex is more difficult to find. Which form would you use in different situations? How can you convert one form into another? To explore the answers to these questions and more, go to.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35389\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-16.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 16\" width=\"364\" height=\"279\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-16.png 364w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-16-300x230.png 300w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Chapter_Review\"><\/a>Solving Quadratic Equations Chapter Review<\/h3>\n<p><strong>9.1 Properties of Radicals (pp. 479\u2013488)<\/strong><\/p>\n<p>Simplify the expression.<br \/>\nQuestion 1.<br \/>\n\\(\\sqrt{72 p^{7}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{72 p^{7}}\\)<br \/>\n= \\(\\sqrt{72 p^{6} p^{1}}\\)<br \/>\n= \\(\\sqrt{36 p^{6} \u00d7 2p^{1}}\\)<br \/>\n= 6p\u00b3 \\(\\sqrt{2p}\\)<\/p>\n<p>Question 2.<br \/>\n\\(\\sqrt{\\frac{45}{7 y}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{\\frac{45}{7 y}}\\)<br \/>\n= \\(\\frac{\\sqrt{45}}{\\sqrt{7 y}}\\)<br \/>\n= \\(\\frac{\\sqrt{5 (9)}}{\\sqrt{7 y}}\\)<br \/>\n= 3\\(\\sqrt{\\frac{5}{7 y}}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt[3]{\\frac{125 x^{11}}{4}}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt[3]{\\frac{125 x^{11}}{4}}\\)<br \/>\n= \\(\\sqrt[3]{\\frac{5 ^{3} x^{9} x^{2}}{4}}\\)<br \/>\n= 5x\u00b3\\(\\sqrt[3]{\\frac{ x^{2}}{4}}\\)<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{8}{\\sqrt{6}+2}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{8}{\\sqrt{6}+2}\\)<br \/>\nMultiply and divide the given expression with \\(\\sqrt{6} &#8211; 2\\)<br \/>\n= \\(\\frac{8}{\\sqrt{6}+2}\\) \u00d7 \\(\\frac{\\sqrt{6} &#8211; 2}{\\sqrt{6} &#8211; 2}\\)<br \/>\n= \\(\\frac{8 (\\sqrt{6} &#8211; 2} {6 &#8211; 4}\\)<br \/>\n= \\(\\frac{8\\sqrt{6} &#8211; 2}{2}\\)<br \/>\n= 4 \\(\\sqrt{6} &#8211; 2\\)<\/p>\n<p>Question 5.<br \/>\n4\\(\\sqrt{3}\\) + 5\\(\\sqrt{12}\\)<br \/>\nAnswer:<br \/>\n4\\(\\sqrt{3}\\) + 5\\(\\sqrt{12}\\)<br \/>\n= 4\\(\\sqrt{3}\\) + 5\\(\\sqrt{4 (3)}\\)<br \/>\n= 4\\(\\sqrt{3}\\) + 5 (2)\\(\\sqrt{3}\\)<br \/>\n= 4\\(\\sqrt{3}\\) + 10\\(\\sqrt{3}\\)<br \/>\n= \\(\\sqrt{3}\\) (5 + 4)<br \/>\n= 9\\(\\sqrt{3}\\)<\/p>\n<p>Question 6.<br \/>\n15\\(\\sqrt [ 3 ]{ 2 }\\) &#8211; 2\\(\\sqrt [ 3 ]{ 54 }\\)<br \/>\nAnswer:<br \/>\n15\\(\\sqrt [ 3 ]{ 2 }\\) &#8211; 2\\(\\sqrt [ 3 ]{ 54 }\\)<br \/>\n= 15\\(\\sqrt [ 3 ]{ 2 }\\) &#8211; 2\\(\\sqrt [ 3 ]{ 27 (2) }\\)<br \/>\n= 15\\(\\sqrt [ 3 ]{ 2 }\\) &#8211; 2 (3)\\(\\sqrt [ 3 ]{ 2 }\\)<br \/>\n= 15\\(\\sqrt [ 3 ]{ 2 }\\) &#8211; 6\\(\\sqrt [ 3 ]{ 2 }\\)<br \/>\n= [\/latex]\\sqrt[3]{2}[\/latex] (15 &#8211; 6)<br \/>\n= 9 \\(\\sqrt[3]{2}\\)<\/p>\n<p>Question 7.<br \/>\n(3\\(\\sqrt{7}\\) + 5)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n(3\\(\\sqrt{7}\\) + 5)<sup>2<\/sup><br \/>\n= (3\\(\\sqrt{7}\\))\u00b2 + 5\u00b2 + 2 (3\\(\\sqrt{7}\\)) (5)<br \/>\n= 9 (7) + 25 + 30\\(\\sqrt{7}\\)<br \/>\n= 88 + 30\\(\\sqrt{7}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt{6}\\)(\\(\\sqrt{18}\\) + \\(\\sqrt{8}\\))<br \/>\nAnswer:<br \/>\n\\(\\sqrt{6}\\)(\\(\\sqrt{18}\\) + \\(\\sqrt{8}\\))<br \/>\n= \\(\\sqrt{6}\\)(\\(\\sqrt{9 (2)}\\) + \\(\\sqrt{4 (2)}\\))<br \/>\n= \\(\\sqrt{6}\\)(\\(3\\sqrt{2}\\) + \\(2\\sqrt{2}\\))<br \/>\n= \\(\\sqrt{6}\\)((3 + 2) \\(\\sqrt{2}\\))<br \/>\n= \\(\\sqrt{6}\\) (5\\(\\sqrt{2}\\))<br \/>\n= 5 \\(\\sqrt{12}\\)<br \/>\n= 5 \\(\\sqrt{4 (3)}\\)<br \/>\n= 10 \\(\\sqrt{3}\\)<\/p>\n<p><strong>9.2 Solving Quadratic Equations by Graphing (pp. 489\u2013496)<\/strong><\/p>\n<p><strong>Solve the equation by graphing<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35390\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-cr-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations cr 9\" width=\"279\" height=\"191\" \/><br \/>\nQuestion 9.<br \/>\nx<sup>2<\/sup> &#8211; 9x + 18 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115683\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-115.png\" alt=\"\" width=\"485\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-115.png 485w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-115-289x300.png 289w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nThe solutions of the given equation are 3 and 6<\/p>\n<p>Question 10.<br \/>\nx<sup>2<\/sup> &#8211; 2x = -4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115685\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-116.png\" alt=\"\" width=\"484\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-116.png 484w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-116-288x300.png 288w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><br \/>\nThere are no real solutions for the given equation as there are no x-intercepts<\/p>\n<p>Question 11.<br \/>\n-8x &#8211; 16 = x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115686\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-117.png\" alt=\"\" width=\"485\" height=\"497\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-117.png 485w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-117-293x300.png 293w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nThe solution for the given equation is -4<\/p>\n<p>Question 12.<br \/>\nThe graph of f(x) = (x + 1)(x<sup>2<\/sup> + 2x &#8211; 3) is shown. Find the zeros of f.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35390\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-cr-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations cr 9\" width=\"279\" height=\"191\" \/><br \/>\nAnswer:<br \/>\nf (x) = (x + 1) (x\u00b2 + 2x &#8211; 3)<br \/>\nf (x) = 0<br \/>\n(x + 1) (x\u00b2\u00a0 + 2x &#8211; 3) = 0<br \/>\nx + 1 = 0 or x\u00b2 + 2x &#8211; 3 = 0<br \/>\nx + 1 = 0 or x\u00b2 + 3x &#8211; x &#8211; 3 = 0<br \/>\nx = -1 or x (x + 3) &#8211; 1(x + 3) = 0<br \/>\nx = -1 or (x\u00a0 1) (x + 3) = 0<br \/>\nx = -1 or x &#8211; 1 = 0 or x + 3 = 0<br \/>\nx = -1 or x = 1 or x = -3<br \/>\nThe zeroes of the given function is -1, 1, and -3<\/p>\n<p>Question 13.<br \/>\nGraph f(x) = x<sup>2<\/sup> + 2x &#8211; 5. Approximate the zeros of f to the nearest tenth.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115688\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-118.png\" alt=\"\" width=\"475\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-118.png 475w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-118-283x300.png 283w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><br \/>\nThe approximate solution of the given function is (-4, 2)<\/p>\n<p><strong>9.3 Solving Quadratic Equations Using Square Roots (pp. 497\u2013502)<\/strong><\/p>\n<p><strong>Solve the equation using square roots. Round your solutions to the nearest hundredth, if necessary.<\/strong><br \/>\nQuestion 14.<br \/>\nx<sup>2<\/sup> + 5 = 17<br \/>\nAnswer:<br \/>\nx\u00b2 + 5 = 17<br \/>\nx\u00b2+ 5 &#8211; 5 = 17 &#8211; 5<br \/>\nx\u00b2 = 12<br \/>\n\u221ax\u00b2 = \u221a12<br \/>\nx = \u00b1\u221a12<br \/>\n\u221a12 = 3.46<br \/>\nx = \u00b13.46<\/p>\n<p>Question 15.<br \/>\nx<sup>2<\/sup> &#8211; 14 = -14<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 14 = -14<br \/>\nx\u00b2 &#8211; 14 + 14 = -14 + 1 4<br \/>\nx\u00b2 = 0<br \/>\n\u221ax\u00b2 = \u221a0<br \/>\nx = 0<\/p>\n<p>Question 16.<br \/>\n(x + 2)<sup>2<\/sup> = 64<br \/>\nAnswer:<br \/>\n(x + 2)\u00b2 = 64<br \/>\n\u221a(x + 2)\u00b2 = \u221a64<br \/>\nx + 2 = \u00b18<br \/>\nx + 2 = 8 or x + 2 = -8<br \/>\nx = 8 &#8211; 2 or x = -8 &#8211; 2<br \/>\nx = 6 or x = -10<\/p>\n<p>Question 17.<br \/>\n4x<sup>2<\/sup> + 25 = -75<br \/>\nAnswer:<br \/>\n4x\u00b2 + 25 = -75<br \/>\n4x\u00b2 + 25 &#8211; 25 = -75 &#8211; 25<br \/>\n4x\u00b2 = -100<br \/>\nx\u00b2 = \\(\\frac{-100}{25}\\)<br \/>\nThe square of a real number will not take any negative number<br \/>\nThere are no real solutions for the given equation<\/p>\n<p>Question 18.<br \/>\n(x &#8211; 1)<sup>2<\/sup> = 0<br \/>\nAnswer:<br \/>\n(x &#8211; 1)\u00b2 = 0<br \/>\n\u221a(x &#8211; 1)\u00b2 = \u221a0<br \/>\nx &#8211; 1 = 0<br \/>\nx = 0 + 1<br \/>\nx = 1<\/p>\n<p>Question 19.<br \/>\n19 = 30 &#8211; 5x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n19 = 30 &#8211; 5x\u00b2<br \/>\n19 &#8211; 19 = 30 &#8211; 19 &#8211; 5x\u00b2<br \/>\n0 = 11 &#8211; 5x\u00b2<br \/>\n5x\u00b2 = 11<br \/>\nx\u00b2 = \\(\\frac{11}{5}\\)<br \/>\n\u221ax\u00b2 = \u221a\\(\\frac{11}{5}\\)<br \/>\nx = \u00b1\\(\\frac{11}{5}\\)<br \/>\n\\(\\frac{11}{5}\\) = 2.20<br \/>\nx = \u00b12.20<\/p>\n<p><strong>9.4 Solving Quadratic Equations by Completing the Square (pp. 505\u2013514)<\/strong><\/p>\n<p><strong>Solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.<\/strong><br \/>\nQuestion 20.<br \/>\nx<sup>2<\/sup> + 6x &#8211; 40 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 + 6x &#8211; 40 = 0<br \/>\n4\u00b2 + 6x &#8211; 40 + 40 = 40 + 0<br \/>\nx\u00b2 + 6x = 40<br \/>\nax\u00b2 + b = d<br \/>\nc = (\\(\\frac{b}{2}\\))\u00b2<br \/>\nax\u00b2 + bx + c = d<br \/>\nx\u00b2 + 6x + (\\(\\frac{6}{2}\\))\u00b2 = 40 + (\\(\\frac{6}{2}\\))\u00b2<br \/>\nx\u00b2 + 6x + 9 = 40 + 9<br \/>\n(x + 3)\u00b2 = 49<br \/>\n\u221a(x + 3)\u00b2 = \u221a49<br \/>\nx + 3 = 7 or x + 3 = -7<br \/>\nx = 7 &#8211; 3 or x = -7 &#8211; 3<br \/>\nx = 4 or x = -10<\/p>\n<p>Question 21.<br \/>\nx<sup>2<\/sup> + 2x + 5 = 4<br \/>\nAnswer:<br \/>\nx\u00b2 + 2x + 5 = 4<br \/>\nx\u00b2+ 2x + 5 &#8211; 5 = 4 &#8211; 5<br \/>\nx\u00b2+ 2x = -1<br \/>\nax\u00b2 + bx = d<br \/>\nc = (\\(\\frac{b}{2}\\))\u00b2<br \/>\nax\u00b2 + bx + c = d<br \/>\nx\u00b2 + 2x + (\\(\\frac{2}{2}\\))\u00b2 = -1 + (\\(\\frac{2}{2}\\))\u00b2<br \/>\nx\u00b2 + 2x + 1 = -1 + 1<br \/>\n(x + 1)\u00b2 = 0<br \/>\n\u221a(x + 1)\u00b2 = \u221a0<br \/>\nx + 1 = 0<br \/>\nx = -1<\/p>\n<p>Question 22.<br \/>\n2x<sup>2<\/sup> &#8211; 4x = 10<br \/>\nAnswer:<br \/>\n2x\u00b2 &#8211; 4x = 10<br \/>\nx\u00b2 &#8211; 2x = 5<br \/>\nax\u00b2 + bx = d<br \/>\nc = (\\(\\frac{b}{2}\\))\u00b2<br \/>\nax\u00b2 + bx + c = d<br \/>\nx\u00b2 &#8211; 2x + 1 = 5 + 1<br \/>\n(x &#8211; 1)\u00b2 = 6<br \/>\n\u221a(x &#8211; 1)\u00b2 = \u221a6<br \/>\nx &#8211; 1 = \u00b1\u221a6<br \/>\n\u221a6 = 2.44<br \/>\nx = 2.44 + 1 or x = -2.44 + 1<br \/>\nx = 3.44 or x = -1.44<\/p>\n<p>Determine whether the quadratic function has a maximum or minimum value. Then find the value.<br \/>\nQuestion 23.<br \/>\ny = -x<sup>2<\/sup> + 6x &#8211; 1<br \/>\nAnswer:<br \/>\ny = -x\u00b2+ 6x &#8211; 1<br \/>\ny + 1 = -x\u00b2 + 6x &#8211; 1 + 1<br \/>\ny + 1 = -(x\u00b2 &#8211; 6x)<br \/>\nc = (\\(\\frac{b}{2}\\))\u00b2<br \/>\ny + 1 &#8211; 9 = -(x\u00b2 &#8211; 6x + 9)<br \/>\ny &#8211; 8 = -(x &#8211; 3)\u00b2<br \/>\ny = -(x &#8211; 3)\u00b2 + 8<br \/>\nThe value of a is negative<br \/>\nSince a is negative, the parabola will be closed down and the value of y becomes the maximum value<br \/>\nThe given function has a maximum value and the maximum value is 8<\/p>\n<p>Question 24.<br \/>\nf(x) = x<sup>2<\/sup> + 4x + 11<br \/>\nAnswer:<br \/>\nf (x) = x\u00b2 + 4x + 11<br \/>\nf (x) &#8211; 11 = x\u00b2 + 4x + 11 &#8211; 11<br \/>\nf (x) &#8211; 11 = x\u00b2 + 4x<br \/>\nax\u00b2 + bx = d<br \/>\nc = (\\(\\frac{b}{2}\\))\u00b2<br \/>\nf (x) &#8211; 11 + 4 = x\u00b2 + 4x + 4<br \/>\nf (x) &#8211; 7 = (x + 2)\u00b2<br \/>\nf (x) = (x + 2)\u00b2 + 7<br \/>\nThe value of a is positive<br \/>\nSince a is positive, the parabola will be open up and the value of y becomes the minimum value<br \/>\nThe given function has a minimum value and the minimum value is 7<\/p>\n<p>Question 25.<br \/>\ny = 3x<sup>2<\/sup> &#8211; 24x + 15<br \/>\nAnswer:<br \/>\ny = 3x\u00b2 &#8211; 24x + 15<br \/>\ny &#8211; 15 = 3x\u00b2 &#8211; 24x + 15 &#8211; 15<br \/>\ny &#8211; 15 = 3x\u00b2 &#8211; 24x<br \/>\ny &#8211; 15 = 3 (x\u00b2 &#8211; 8x)<br \/>\nax\u00b2 + bx = d<br \/>\nc = (\\(\\frac{b}{2}\\))\u00b2<br \/>\ny &#8211; 15 + 144 = 3(x\u00b2 &#8211; 8x + 48)<br \/>\ny + 129 = 3 (x &#8211; 12)\u00b2<br \/>\ny = 3 (x &#8211; 12)\u00b2 &#8211; 129<br \/>\nThe value of a is negative<br \/>\nSince a is negative, the parabola will be closed down and the value of y becomes the maximum value<br \/>\nThe given function has a maximum value and the maximum value is -129<\/p>\n<p>Question 26.<br \/>\nThe width w of a credit card is 3 centimeters shorter than the length \u2113. The area is 46.75 square centimeters. Find the perimeter.<br \/>\nAnswer:<br \/>\nLet the length of a credit card be x cm<br \/>\nThe width of a credit card is: (x &#8211; 3) cm<br \/>\n46.75 = x (x &#8211; 3)<br \/>\nx\u00b2 &#8211; 3x = 46.75<br \/>\nx\u00b2 &#8211; 3x &#8211; 46.75 = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115701\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-119.png\" alt=\"\" width=\"487\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-119.png 487w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-119-290x300.png 290w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><br \/>\nThe solutions of x are -6 and 8<br \/>\nThe length will not be negative,<br \/>\nThe length of the credit card is 8 cm<br \/>\nThe width of the credit card is 8 &#8211; 3 = 5 cm<br \/>\nThe perimeter of the credit card = 2 (l + b)<br \/>\n= 2 (8 + 5) = 2 (13) = 26 cm<br \/>\nThe perimeter of the credit card is 26 cm<\/p>\n<p><strong>9.5 Solving Quadratic Equations Using the Quadratic Formula (pp. 515\u2013524)<\/strong><\/p>\n<p><strong>Solve the equation using the Quadratic Formula. Round your solutions to the nearest tenth, if necessary.<\/strong><br \/>\nQuestion 27.<br \/>\nx<sup>2<\/sup>+ 2x &#8211; 15 = 0<br \/>\nAnswer;<br \/>\nx\u00b2 + 2x &#8211; 15 = 0<br \/>\nax\u00b2+ bx + c = 0<br \/>\na = 1, b = 2, and c = -15<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{-2 \u00b1 \\sqrt{2\u00b2 + 4 (1) (15)}}{2 (1)}\\)<br \/>\nx = \\(\\frac{-2 \u00b1 \\sqrt{64}}{2}\\)<br \/>\nx = \\(\\frac{-2 \u00b1 8}{2}\\)<br \/>\nx = 3 or x = -5<\/p>\n<p>Question 28.<br \/>\n2x<sup>2<\/sup> &#8211; x + 8 = 16<br \/>\nAnswer:<br \/>\n2x\u00b2 &#8211; x + 8 = 0<br \/>\nax\u00b2+ bx + c = 0<br \/>\na = 2, b = -1, and c = 8<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{1 \u00b1 \\sqrt{(-1)\u00b2 &#8211; 4 (2) (8)}}{2 (2)}\\)<br \/>\nx = \\(\\frac{1 \u00b1 \\sqrt{-63}}{4}\\)<br \/>\nThe square of a real number will not be a negative number<br \/>\nThere are no real solutions for the given equation<\/p>\n<p>Question 29.<br \/>\n-5x<sup>2<\/sup> + 10x = 5<br \/>\nAnswer;<br \/>\n-5x\u00b2 + 10x = 5<br \/>\n5x\u00b2 &#8211; 10x + 5 = 0<br \/>\nx\u00b2 &#8211; 2x + 1 = 0<br \/>\nax\u00b2+ bx + c = 0<br \/>\na = 1, b = -2, and c = 1<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{2 \u00b1 \\sqrt{(-2)\u00b2 &#8211; 4 (1) (1)}}{2 (1)}\\)<br \/>\nx = \\(\\frac{2 \u00b1 \\sqrt{0}}{2}\\)<br \/>\nx = \\(\\frac{2}{2}\\)<br \/>\nx = 1<\/p>\n<p>Find the number of x-intercepts of the graph of the function.<br \/>\nQuestion 30.<br \/>\ny = -x<sup>2<\/sup> + 6x &#8211; 9<br \/>\nAnswer:<br \/>\ny = -x\u00b2 + 6x &#8211; 9<br \/>\nTo find the x-interxept,<br \/>\nPut y = 0<br \/>\n-x\u00b2 + 6x &#8211; 9 = 0<br \/>\nx\u00b2 &#8211; 6x + 9 = 0<br \/>\nx\u00b2 &#8211; 3x &#8211; 3x + 9 = 0<br \/>\nx (x &#8211; 3) &#8211; 3 (x &#8211; 3) = 0<br \/>\n(x &#8211; 3) (x &#8211; 3) = 0<br \/>\nx &#8211; 3 = 0 or x &#8211; 3 = 0<br \/>\nx = 3 or x = 3<\/p>\n<p>Question 31.<br \/>\ny = 2x<sup>2<\/sup> + 4x + 8<br \/>\nAnswer:<br \/>\ny = 2x\u00b2 + 4x + 8<br \/>\nTo find the x-intercept,<br \/>\nPut y = 0<br \/>\n2x\u00b2 + 4x + 8 = 0<br \/>\nx\u00b2 + 2x + 4 = 0<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 1, b = 2, and c = 4<br \/>\nx = \\(\\frac{-b \u00b1 \\sqrt{b\u00b2 &#8211; 4ac}}{2a}\\)<br \/>\nx = \\(\\frac{-2 \u00b1 \\sqrt{2\u00b2 &#8211; 4 (1) (4)}}{2 (1)}\\)<br \/>\nx = \\(\\frac{-2 \u00b1 \\sqrt{-12}}{2a}\\)<br \/>\nThe square of a real number will not take any negative values<br \/>\nThere are no solutions for the given equation<\/p>\n<p>Question 32.<br \/>\ny = &#8211; \\(\\frac{1}{2}\\)x<sup>2<\/sup> + 2x<br \/>\nAnswer:<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x\u00b2 + 2x<br \/>\nTo find the x-intercept,<br \/>\nPut y = 0<br \/>\n&#8211; \\(\\frac{1}{2}\\)x<sup>2<\/sup> + 2x = 0<br \/>\n&#8211; \\(\\frac{1}{2}\\)x<sup>2<\/sup> = &#8211; 2x<br \/>\n\\(\\frac{1}{2}\\)x<sup>2<\/sup> = 2x<br \/>\nx = 2 (2)<br \/>\nx = 4<br \/>\nThe solution for the given equation is 4<\/p>\n<p><strong>9.6 Solving Nonlinear Systems of Equations (pp. 525\u2013532)<\/strong><\/p>\n<p><strong>Solve the system using any method.<\/strong><br \/>\nQuestion 33.<br \/>\ny = x<sup>2<\/sup> &#8211; 2x &#8211; 4<br \/>\ny = -5<br \/>\nAnswer:<br \/>\ny = x\u00b2 &#8211; 2x &#8211; 4<br \/>\ny = 5<br \/>\nx\u00b2 &#8211; 2x &#8211; 4 = 5<br \/>\nx\u00b2 &#8211; 2x = 5 + 4<br \/>\nx\u00b2 &#8211; 2x = 9<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115711\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-120.png\" alt=\"\" width=\"479\" height=\"504\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-120.png 479w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-120-285x300.png 285w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nThe solutions for the given system of equations are -2 and 4<\/p>\n<p>Question 34.<br \/>\ny = x<sup>2<\/sup> &#8211; 9<br \/>\ny = 2x + 5<br \/>\nAnswer:<br \/>\ny = x\u00b2 &#8211; 9<br \/>\ny = 2x + 5<br \/>\nx\u00b2 &#8211; 9 = 2x + 5<br \/>\nx\u00b2 &#8211; 2x &#8211; 9 &#8211; 5 = 0<br \/>\nx\u00b2 &#8211; 2x &#8211; 14 = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115713\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-122.png\" alt=\"\" width=\"515\" height=\"396\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-122.png 515w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-122-300x231.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<p>Question 35.<br \/>\ny = 2(\\(\\frac{1}{2}\\))<sup>x<\/sup> &#8211; 5<br \/>\ny = -x<sup>2<\/sup> &#8211; x + 4<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Chapter_Test\"><\/a>Solving Quadratic Equations Chapter Test<\/h3>\n<p><strong>Solve the equation using any method. Explain your choice of method.<\/strong><br \/>\nQuestion 1.<br \/>\nx<sup>2<\/sup> &#8211; 121 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 = 121 = 0<br \/>\nx\u00b2 &#8211; 121 + 121 = 0 + 121<br \/>\nx\u00b2 = 121<br \/>\n\u221ax\u00b2 = \u221a121<br \/>\nx = \u00b111<\/p>\n<p>Question 2.<br \/>\nx<sup>2<\/sup> &#8211; 6x = 10<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 6x = 10<br \/>\nx\u00b2 &#8211; 6x + 9 = 10 + 9<br \/>\n(x &#8211; 3)\u00b2 = 19<br \/>\n\u221a(x &#8211; 3)\u00b2 = \u221a19<br \/>\nx &#8211; 3 = \u00b1\u221a19<br \/>\nWe know that,<br \/>\n\u221a19 = 4.35<br \/>\nSo,<br \/>\nx = 4.35 + 3 or x = -4.35 + 3<br \/>\nx = 7.35 or x = -1.35<\/p>\n<p>Question 3.<br \/>\n-2x<sup>2<\/sup> + 3x + 7 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115720\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-123.png\" alt=\"\" width=\"504\" height=\"416\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-123.png 504w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-123-300x248.png 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/p>\n<p>Question 4.<br \/>\nx<sup>2<\/sup> &#8211; 7x + 12 = 0<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 7x + 12 = 0<br \/>\nx\u00b2 &#8211; 4x &#8211; 3x + 12 = 0<br \/>\nx (x &#8211; 4) &#8211; 3 (x &#8211; 4) = 0<br \/>\n(x &#8211; 3) (x &#8211; 4) = 0<br \/>\nx &#8211; 3 = 0 or x &#8211; 4 = 0<br \/>\nx = 3 or x = 4<\/p>\n<p>Question 5.<br \/>\n5x<sup>2<\/sup> + x &#8211; 4 = 0<br \/>\nAnswer:<br \/>\n5x\u00b2 + x &#8211; 4 = 0<br \/>\n5x\u00b2 + 5x &#8211; 4x &#8211; 4 = 0<br \/>\n5x (x + 1) &#8211; 4 (x + 1) = 0<br \/>\n(5x &#8211; 4) (x + 1) = 0<br \/>\n5x &#8211; 4 = 0 or x + 1 = 0<br \/>\n5x = 4 or x = -1<br \/>\nx = \\(\\frac{4}{5}\\) or x = -1<\/p>\n<p>Question 6.<br \/>\n(4x + 3)<sup>2<\/sup> = 16<br \/>\nAnswer:<br \/>\n(4x + 3)\u00b2 = 16<br \/>\n\u221a(4x + 3)\u00b2 = \u221a16<br \/>\n4x + 3 = 4 or 4x + 3 = -4<br \/>\n4x = 4 &#8211; 3 or 4x = -4 &#8211; 3<br \/>\n4x = 1 or 4x = -7<br \/>\nx = \\(\\frac{1}{4}\\) or x = &#8211;\\(\\frac{7}{4}\\)<\/p>\n<p>Question 7.<br \/>\nDescribe how you can use the method of completing the square to determine whether the function f(x) = 2x<sup>2<\/sup> + 4x &#8211; 6 can be represented by the graph shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35391\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-ct-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations ct 7\" width=\"141\" height=\"145\" \/><br \/>\nAnswer:<br \/>\nf (x) = 2x\u00b2 + 4x &#8211; 6<br \/>\nWe have to make f (x) = 0<br \/>\n2x\u00b2+ 4x &#8211; 6 = 0<br \/>\n2x\u00b2+ 4x &#8211; 6 + 6 = 0 + 6<br \/>\n2x\u00b2 + 4x = 6<br \/>\nx\u00b2+ 2x = 3<br \/>\n\\(\\frac{b}{2}\\) = \\(\\frac{2}{2}\\)<br \/>\n= 1<br \/>\nx\u00b2+ 2x + 1 = 3 + 1<br \/>\n(x + 1)\u00b2 = 4<br \/>\n\u221a(x + 1)\u00b2 = \u221a4<br \/>\nx + 1 = 2 or x + 1 = -2<br \/>\nx = 2 &#8211; 1 or x = -2 &#8211; 1<br \/>\nx = 1 or x = -3<\/p>\n<p>Question 8.<br \/>\nWrite an expression involving radicals in which a conjugate can be used to simplify the expression.<br \/>\nAnswer:<br \/>\nThe expression that involves radicals in which a conjugate can be used to simplify the expression is<br \/>\n\\(\\frac{8}{3 + \\sqrt{6}}\\)<br \/>\nThe conjugate of the above expression is<br \/>\n\\(\\frac{3 &#8211; \\sqrt{6}}\\)<\/p>\n<p><strong>Solve the system using any method.<\/strong><br \/>\nQuestion 9.<br \/>\ny = x<sup>2<\/sup> &#8211; 4x &#8211; 2<br \/>\ny = -4x + 2<br \/>\nAnswer:<br \/>\ny = x\u00b2 &#8211; 4x &#8211; 2<br \/>\ny = -4x + 2<br \/>\nx\u00b2 &#8211; 4x &#8211; 2 = -4x + 2<br \/>\nx\u00b2 &#8211; 4x &#8211; 2 + 4x &#8211; 2 = 0<br \/>\nx\u00b2 &#8211; 4 = 0<br \/>\nx\u00b2 = 4<br \/>\n\u221ax\u00b2 = \u221a4<br \/>\nx = 2 or x = -2<\/p>\n<p>Question 10.<br \/>\ny = -5x<sup>2<\/sup> + x &#8211; 1<br \/>\ny = -7<br \/>\nAnswer:<br \/>\ny = -5x\u00b2+ x &#8211; 1<br \/>\ny = -7<br \/>\n-5x\u00b2 + x &#8211; 1 = -7<br \/>\n-5x\u00b2 + x &#8211; 1 + 7 = 0<br \/>\n-5x\u00b2 +x + 6 = 0<br \/>\n-5x\u00b2 + 6x &#8211; 5x + 6 = 0<br \/>\n-5x(x + 1) + 6 (x + 1) = 0<br \/>\n(-5x + 6) (x + 1) = 0<br \/>\n-5x + 6 = 0 or x + 1 = 0<br \/>\n-5x = -6 or x = -1<br \/>\nx = \\(\\frac{6}{5}\\) or x = -1<\/p>\n<p>Question 11.<br \/>\ny = \\(\\frac{1}{2}\\)(4)<sup>x<\/sup> + 1<br \/>\ny = x<sup>2<\/sup> &#8211; 2x + 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115721\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-124.png\" alt=\"\" width=\"490\" height=\"538\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-124.png 490w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-124-273x300.png 273w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nThe solution for the given set of equations is (3, 1)<\/p>\n<p>Question 12.<br \/>\nA skier leaves an 8-foot-tall ramp with an initial vertical velocity of 28 feet per second. The function h = -16t<sup>2<\/sup> + 28t + 8 represents the height h (in feet) of the skier after t seconds. The skier has a perfect landing. How many points does the skier earn?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35392\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-ct-12.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations ct 12\" width=\"260\" height=\"120\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115723\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-125.png\" alt=\"\" width=\"615\" height=\"953\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-125.png 615w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-125-194x300.png 194w\" sizes=\"(max-width: 615px) 100vw, 615px\" \/><\/p>\n<p>Question 13.<br \/>\nAn amusement park ride lifts seated riders 265 feet above the ground. The riders are then dropped and experience free fall until the brakes are activated 105 feet above the ground. The function h = -16t<sup>2<\/sup> + 265 represents the height h (in feet) of the riders t seconds after they are dropped. How long do the riders experience free fall? Round your solution to the nearest hundredth.<br \/>\nAnswer:<br \/>\nThe function h = -16t<sup>2<\/sup> + 265 represents the height h (in feet) of the riders t seconds after they are dropped.<br \/>\n105 = -16t<sup>2<\/sup> + 265<br \/>\n0 = 16t<sup>2<\/sup> + 160<br \/>\nt<sup>2<\/sup> &#8211; 10 = 0<br \/>\nt = \u221a10<\/p>\n<p>Question 14.<br \/>\nWrite an expression in the simplest form that represents the area of the painting shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35393\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-ct-14.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations ct 14\" width=\"265\" height=\"116\" \/><br \/>\nAnswer:<br \/>\nThe area of the painting = \\(\\sqrt{30 x^{7}}\\) \u00d7\\(\\frac{36}{\\sqrt{3}}\\)<br \/>\n= \\(\\sqrt{10 (3) x^{6} x}\\) \u00d7\\(\\frac{36}{\\sqrt{3}}\\)<br \/>\n= x\u00b3 \\(\\sqrt{10}\\) \u00d7 \\(\\sqrt{3}\\) \u00d7 \\(\\frac{36}{\\sqrt{3}}\\)<br \/>\n= 36x\u00b3 \\(\\sqrt{10}\\)<\/p>\n<p>Question 15.<br \/>\nExplain how you can determine the number of times the graph of y = 5x<sup>2<\/sup> &#8211; 10x + 5 intersects the x-axis without graphing or solving an equation.<br \/>\nAnswer:<br \/>\ny = 5x\u00b2 &#8211; 10x + 5<br \/>\nWe can determine the number of times the graph of the given equation intersects the x-axis by using the discriminant<br \/>\nDiscriminant (d) = b\u00b2 &#8211; 4ac<br \/>\nb\u00b2 &#8211; 4ac &gt; 0 &#8212;&#8212;&gt; 2 intersection points<br \/>\nb\u00b2 &#8211; 4ac = 0 &#8212;&#8212;-&gt; 1 intersection point<br \/>\nb\u00b2 &#8211; 4ac &lt; 0 &#8212;&#8212;-&gt; No intersection points<br \/>\nax\u00b2 + bx + c = 0<br \/>\na = 5, b = -10, and c = 5<br \/>\nb\u00b2 &#8211; 4ac = (-10)\u00b2 &#8211; 4 (5) (5)<br \/>\n= 100 &#8211; 100<br \/>\n= 0<\/p>\n<p>Question 16.<br \/>\nConsider the quadratic equation ax<sup>2<\/sup> + bx + c = 0 Find values of a, b, and c so that the graph of its related function has (a) two\u00a0 x-intercepts, (b) one x-intercepts.and (c) no x-intercepts.<br \/>\nAnswer:<br \/>\nax\u00b2 + bx + c = 0<br \/>\nb\u00b2 &#8211; 4ac &gt; 0 &#8212;&#8212;&gt; 2 x-intercepts<br \/>\nb\u00b2 &#8211; 4ac = 0 &#8212;&#8212;-&gt; 1 x-intercept<br \/>\nb\u00b2 &#8211; 4ac &lt; 0 &#8212;&#8212;-&gt; No x-intercepts<br \/>\na) For 2 x-intercepts:<br \/>\nb\u00b2 &#8211; 4ac &gt; 0<br \/>\nb\u00b2 &gt; 4ac<br \/>\n4ac &lt; b\u00b2<br \/>\nc &lt; \\(\\frac{b\u00b2}{4a}\\)<br \/>\nb) For 1 x-intercept:<br \/>\nb\u00b2 &#8211; 4ac = 0<br \/>\nb\u00b2 = 4ac<br \/>\n4ac = b\u00b2<br \/>\nc = \\(\\frac{b\u00b2}{4a}\\)<br \/>\nc) For no x-intercepts:<br \/>\nb\u00b2 &#8211; 4ac &lt; 0<br \/>\nb\u00b2 &lt; 4ac<br \/>\n4ac &gt; b\u00b2<br \/>\nc &gt; \\(\\frac{b\u00b2}{4a}\\)<\/p>\n<p>Question 17.<br \/>\nThe numbers y of two types of bacteria after x hours are represented by the models below.<br \/>\ny = 3x<sup>2<\/sup> + 8x + 20 Type A<br \/>\ny = 27x + 60 Type B<br \/>\na. When are there 400 Type A bacteria?<br \/>\nb. When are the number of Type A and Type B bacteria the same?<br \/>\nc. When are there more Type A bacteria than Type B? When are there more Type B bacteria than Type A? Use a graph to support your answer.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Cumulative_Assessment\"><\/a>Solving Quadratic Equations Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nThe graphs of four quadratic functions are shown. Determine whether the discriminants of the equations formed by setting each function equal to zero are positive, negative, or zero.f(x) = 0, g(x) = 0, h(x) = 0, and j(x) = 0<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35394\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations ca 1\" width=\"190\" height=\"190\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-1.png 190w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-1-150x150.png 150w\" sizes=\"(max-width: 190px) 100vw, 190px\" \/><br \/>\nAnswer:<br \/>\nDiscriminant (d) = b\u00b2 &#8211; 4ac<br \/>\nd &gt; 0, then the equation will have 2 solutions<br \/>\nIf d = 0, then the equation will have 1 solution<br \/>\nIf d &lt; 0, then the equation will have no solutions<br \/>\nFor f (x) = 0,<br \/>\nf (x) will not have any solutions since it did not touch the x-axis<br \/>\nFor g (x) = 0,<br \/>\ng (x) will have 2 solutions since it touched the x-axis at 2 points<br \/>\nFor h (x) = 0,<br \/>\nh (x) will have only 1 solution since it touched the x-axis at only 1 point<br \/>\nFor j (x) = 0,<br \/>\nj (x) will have only 1 solution since it touched the x-axis at only 1 point<\/p>\n<p>Question 2.<br \/>\nThe function f(x) = a(1.08)<sup>x<\/sup> represents the total amount of money (in dollars) in Account A after x years. The function g(x) = 600(b)<sup>x<\/sup> represents the total amount of money (in dollars) in Account B after x years. Fill in values for a and b so that each statement is true.<br \/>\na. When a = ____ and b = ____, Account B has a greater initial amount and increases at a faster rate than Account A.<br \/>\nb. When a = ____ and b = ____, Account B has a lesser initial amount than Account A but increases at a faster rate than Account A.<br \/>\nc. When a = ____ and b = ____, Account B and Account A have the same initial amount, and Account B increases at a slower rate than Account A.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115729\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-126.png\" alt=\"\" width=\"333\" height=\"288\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-126.png 333w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-126-300x259.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/p>\n<p>Question 3.<br \/>\nYour friend claims to be able to find the radius r of each figure, given the surface area S. Do you support your friend\u2019s claim? Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35395\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations ca 3\" width=\"481\" height=\"148\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-3.png 481w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-3-300x92.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\nAnswer:<br \/>\nThe claim of your friend is that we can find the radius r of each figure given the Surface area S<br \/>\nBut,<br \/>\nFor some Surface areas, the variable &#8220;Height (h)&#8221; will be present<br \/>\nWe can find the surface area given radius r only in some cases<br \/>\nThe claim of your friend is not correct<\/p>\n<p>Question 4.<br \/>\nThe tables represent the numbers of items sold at a concession stand on days with different average temperatures. Determine whether the data represented by each table show a positive, negative, or no correlation.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35396\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-4.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations ca 4\" width=\"524\" height=\"157\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-4.png 524w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-4-300x90.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-115730\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-127.png\" alt=\"\" width=\"525\" height=\"520\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-127.png 525w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-127-300x297.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-Chapter-9-127-150x150.png 150w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 5.<br \/>\nWhich graph shows exponential growth?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35397\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-5.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations ca 5\" width=\"483\" height=\"391\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-5.png 483w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-5-300x243.png 300w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><br \/>\nAnswer:<br \/>\nThe graph of an &#8220;Exponential function&#8221; will gradually increase or decrease<br \/>\nGraph A shows the gradual increase<br \/>\nGraph B shows the gradual decrease<br \/>\nGraph A and graph B show the exponential growth<\/p>\n<p>Question 6.<br \/>\nWhich statement best describes the solution(s) of the system of equations?<br \/>\ny = x<sup>2<\/sup> + 2x &#8211; 8<br \/>\ny = 5x + 2<br \/>\nA. The graphs intersect at one point, (-2, -8). So, there is one solution.<br \/>\nB. The graphs intersect at two points, (-2, -8) and (5, 27). So, there are two solutions.<br \/>\nC. The graphs do not intersect. So, there is no solution.<br \/>\nD. The graph of y = x<sup>2<\/sup> + 2x &#8211; 8 has two x-intercepts. So, there are two solutions.<br \/>\nAnswer:<br \/>\ny = x\u00b2 + 2x &#8211; 8<br \/>\ny = 5x + 2<br \/>\nx\u00b2 + 2x &#8211; 8 = 5x + 2<br \/>\nx\u00b2 + 2x &#8211; 5x &#8211; 8 &#8211; 2 = 0<br \/>\nx\u00b2 &#8211; 3x &#8211; 10 = 0<br \/>\nx\u00b2 &#8211; 5x + 2x &#8211; 10 = 0<br \/>\nx (x &#8211; 5) + 2 (x &#8211; 5) = 0<br \/>\n(x + 2) (x &#8211; 5) = 0<br \/>\nx + 2 = 0 or x &#8211; 5 = 0<br \/>\nx = -2 or x = 5<br \/>\nOption D best describes the solutions of the given system of equations<\/p>\n<p>Question 7.<br \/>\nWhich expressions are in the simplest form?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-35398\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-7.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations ca 7\" width=\"433\" height=\"127\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-7.png 433w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-7-300x88.png 300w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><br \/>\nAnswer:<br \/>\nLet the given expressions be named as a, b, c, d, e, f, g, h, i, and j respectively<br \/>\nThe expressions that are in the simplest form are b, d, e, g, i, and j<\/p>\n<p>Question 8.<br \/>\nThe domain of the function shown is all integers in the interval -3 &lt; x \u2264 3. Find all the ordered pairs that are solutions of the equation y = f(x).<br \/>\nf(x) = 4x &#8211; 5<br \/>\nAnswer:<br \/>\nf (x) = 4x &#8211; 5<br \/>\nIt is given that the domain of the given function is<br \/>\n-3 &lt; x \u2264 3<br \/>\nThe domain of the given function = (-2, -1, 0, 1, 2, 3)<br \/>\nFor x = -2, f (-2) = -13<br \/>\nFor x = -1, f (-1) = -9<br \/>\nFor x = 0, f (0) = -5<br \/>\nFor x = 1, f (1) = -1<br \/>\nFor x = 2, f (2) = 3<br \/>\nFor x = 3, f (3) = 7<br \/>\nThe ordered pairs for the given function are (-2, 13), (-1, -9), (0, -5), (1, -1), (2, 3), and (3, 7)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>View Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations with step-by-step explanations from here. Students who are unable to solve quadratic equations can make use of our BIM Algebra 1 Answer Key Ch 9 Solving Quadratic Equation. 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