GEORGIA MATHEMATICS 1 - Carnegie Learning

GEORGIAMATHEMATICS 1Teacher’s Resourcesand Assessments© 2008 Carnegie Learning, Inc.

Pre-TestName ___________________________________________________Date _____________________Identify the values of a, b, and c in each quadratic function.1. y 2x 2 4x 62.y 15 x 2Evaluate each quadratic function for the given value of x. Show all your work.3. f(x) 2x 2 3x 5; f(4)4.g(x) 4x 2 7x; g(2)5. Complete the table of values for the given quadratic function.3y 1 8 x2xy–16–8–40© 2008 Carnegie Learning, Inc.4816Georgia Mathematics 1 Chapter 3 ■ Assessments 225

Pre-Test PAGE 3Name ___________________________________________________Date _____________________8. Write the equation of the line of symmetry for the parabola given by the equationy x 2 6x 14. Show all your work and use a complete sentence in your answer.Find the vertex of the graph of each quadratic function. Then tell whether they-coordinate of the vertex is a minimum or a maximum. Show all your workand use a complete sentence in your answer.9. y 3x 2 24x 710.y 4x 2 323© 2008 Carnegie Learning, Inc.Complete each statement.11. 64 12.13. Approximate 42 to the nearest tenth. Show all your work.16 Georgia Mathematics 1 Chapter 3 ■ Assessments 227

Pre-Test PAGE 414. What x-values do you think will be zeroes of the given quadratic equation?Use complete sentences to explain your reasoning.y 1.25(x 2)(x 2)15. What x-values do you think will be solutions to the given quadratic equation?Write your solutions in radical form if necessary. Use a complete sentence in your answer.x 2 120316. Find the zeroes of the quadratic function by using the Quadratic Formula. Show all your work.y 6x 2 7x 217. What does the value of the discriminant tell you about the number of solutions to aquadratic equation? Use complete sentences in your answer.© 2008 Carnegie Learning, Inc.18. Suppose that a ball is thrown straight up into the air from a height of 5 feet at an initialvelocity of 15 feet per second. Write a quadratic function that models the height of theball in terms of time using the vertical motion model y 16t 2 vt h.228 Chapter 3 ■ Assessments Georgia Mathematics 1

Post-Test PAGE 3Name ___________________________________________________Date _____________________8. Write the equation of the line of symmetry for the parabola given by the equationy 2x 2 16x 10. Show all your work and use a complete sentence in your answer.Find the vertex of the graph of each quadratic function. Then tell whether they-coordinate of the vertex is a minimum or a maximum. Show all your workand use a complete sentence in your answer.9. y x 2 6x 810.y 3x 2 153© 2008 Carnegie Learning, Inc.Complete each statement.11. 36 12.13. Approximate 55 to the nearest tenth. Show all your work.121 Georgia Mathematics 1 Chapter 3 ■ Assessments 231

Post-Test PAGE 414. What x-values do you think will be zeroes of the given quadratic equation?Use complete sentences to explain your reasoning.y 3.5(x 6)(x 6)15. What x-values do you think will be solutions to the given quadratic equation?Write your solutions in radical form if necessary. Use a complete sentence in your answer.x 2 115316. Find the zeroes of the quadratic function using the Quadratic Formula. Show all your work.y 8x 2 9x 117. What does the value of the discriminant tell you about the number of solutions to aquadratic equation? Use complete sentences in your answer.© 2008 Carnegie Learning, Inc.18. Suppose that a ball is thrown straight up into the air from a height of 6 feet at an initialvelocity of 18 feet per second. Write a quadratic function that models the height of theball in terms of time using the vertical motion model y 16t 2 vt h.232 Chapter 3 ■ Assessments Georgia Mathematics 1

Mid-Chapter TestName ___________________________________________________Date _____________________Evaluate each quadratic function for the given value of x. Show all your work.1. g(x) 5x 2 3x 28; g(6)2.h(x) 48 2x 2 ; f(5)Read the scenario below. Use the scenario to answer Questions 3 through 6.The jump of a cricket can be modeled by the function y 3x 2 6x, where x is the horizontaldistance the cricket moves in feet and y is the height of the cricket’s jump in feet.3. Complete the table of values that shows the height of the cricket’s jump as a function ofthe horizontal distance.3LabelsUnitsExpressionsHorizontal distancefeetx00.511.5Heightfeet3x 2 6x© 2008 Carnegie Learning, Inc.2Georgia Mathematics 1 Chapter 3 ■ Assessments 233

Mid-Chapter Test PAGE 24. Create a graph of the quadratic function on the grid below. First, choose your bounds andintervals. Be sure to label your graph clearly.Variable quantity Lower bound Upper bound Interval3(label) (units)(label)5. What is the domain and range of the function in the problem situation? Use a completesentence in your answer.(units)© 2008 Carnegie Learning, Inc.6. Determine the x-intercepts of the graph. Interpret the meaning of the x-intercepts in theproblem situation. Use complete sentences in your answer.234 Chapter 3 ■ Assessments Georgia Mathematics 1

Mid-Chapter Test PAGE 3Name ___________________________________________________Date _____________________Use the quadratic function y = –2x 2 – 4x – 3 for Questions 7 through 9.7. Algebraically determine the line of symmetry and the vertex of the graph. Show all yourwork and use a complete sentence in your answer.8. Draw the graph of the function. Be sure to graph and label the line of symmetry andthe vertex.3© 2008 Carnegie Learning, Inc.Georgia Mathematics 1 Chapter 3 ■ Assessments 235

Mid-Chapter Test PAGE 49. What is the domain and range of the quadratic function? Use a complete sentence inyour answer.Determine whether the vertex of the given quadratic function is a maximum or aminimum. Use a complete sentence to explain your reasoning.10.y 15x 2 2x 2911.y 8x 2 17x 543Complete each statement below.12. 144 13.49 14. Approximate 77 to the nearest tenth. Show all your work.© 2008 Carnegie Learning, Inc.236 Chapter 3 ■ Assessments Georgia Mathematics 1

End of Chapter TestName ___________________________________________________Date _____________________Read the scenario below. Use the scenario to answer Questions 1 through 7.The path of a diver in the water can be modeled by the function y 0.16x 2 3.2x, where x isthe horizontal distance in feet that the diver travels and y is the depth in feet of the diver.1. Complete that table of values that shows the depth as a function of the horizontal distance.LabelsUnitsHorizontal distancefeetDepthfeetExpressionsx 0.16x 2 3.2x0510152032. Write the equation of the line of symmetry. Show all your work and use a completesentence in your answer.© 2008 Carnegie Learning, Inc.3. Find the vertex of the graph of the function. Show all your work and use a completesentence in your answer.Georgia Mathematics 1 Chapter 3 ■ Assessments 237

End of Chapter Test PAGE 24. Create a graph of the quadratic function that models the diver’s path on the grid below.First, choose your bounds and intervals. Be sure to label your graph clearly including theline of symmetry and the vertex.Variable quantity Lower bound Upper bound Interval3(label) (units)(label)5. What is the domain and range of the function in terms of the problem situation?Use complete sentences in your answer.(units)© 2008 Carnegie Learning, Inc.6. Determine the x-intercepts of the graph. Interpret the meaning of the x-intercepts in theproblem situation. Use complete sentences in your answer.238 Chapter 3 ■ Assessments Georgia Mathematics 1

End of Chapter Test PAGE 3Name ___________________________________________________Date _____________________7. How deep is the diver at a horizontal distance of 8 feet? Show all your work and use acomplete sentence in your answer.Determine whether the vertex of the given quadratic function is a maximum or aminimum. Use a complete sentence to explain your reasoning.8.y 7x 2 9x 1039.y 18 6x 210. Approximate 11 to the nearest tenth. Show all your work.© 2008 Carnegie Learning, Inc.Georgia Mathematics 1 Chapter 3 ■ Assessments 239

End of Chapter Test PAGE 4Read the scenario below. Use the scenario to answer Questions 11 through 15.Tanya’s jump rope forms the shape of a parabola as she jumps. The shape can be modeled bythe equation y 2 (x 3)(x 3) , where x is the number of feet to the right of Tanya’s waist,3and y is the height of the jump rope above Tanya’s waist as she swings the rope over her head.11. Create a graph of the quadratic function on the grid below. First, choose your bounds andintervals. Be sure to label your graph clearly.Variable quantity Lower bound Upper bound IntervalHorizontal distance3Height(label) (units)© 2008 Carnegie Learning, Inc.(label)(units)12. What is the y-intercept of the graph? What does it represent in the problem situation?Use complete sentences in your answer.240 Chapter 3 ■ Assessments Georgia Mathematics 1

End of Chapter Test PAGE 5Name ___________________________________________________Date _____________________13. What are the x-intercepts of the graph? What do they represent in the problem situation?Use complete sentences in your answer.14. What is the horizontal distance between the ends of the jump rope? Use a complete sentencein your answer.15. What are the zeroes of this function? Use complete sentences to explain your reasoning.316. What are the solutions to the equation x 2 95? Give your answers in radical form, anduse a complete sentence in your answer.Use the following scenario for Questions 17 through 20.© 2008 Carnegie Learning, Inc.Jude builds a water balloon launcher that launches the balloon straight up. The motion of aballoon that is released by the launcher can be modeled by using the vertical motion modely 16t 2 vt h, where t is the time that the object has been moving in seconds, v isthe initial velocity of the object in feet per second, h is the initial height of the object in feet,and y is the height of the object in feet at time t seconds.17. The launcher is designed to launch the water balloon from a height of 2.75 feet at aninitial velocity of 20 feet per second. Write a quadratic function that models the heightof the water balloon in terms of time.Georgia Mathematics 1 Chapter 3 ■ Assessments 241

End of Chapter Test PAGE 618. Identify a, b, and c, and then find the zeroes of the quadratic function using the QuadraticFormula. Show all your work and use a complete sentence in your answer.319. Would the zeroes have meaning in the problem situation? Use a complete sentencein your answer.20. What is the height of the balloon 0.5 second after launch? Show all your work and use acomplete sentence in your answer.21. What is the discriminant? How does it help you determine the number of solutions to aquadratic equation? Use complete sentences in your answer.© 2008 Carnegie Learning, Inc.242 Chapter 3 ■ Assessments Georgia Mathematics 1

Standardized Test PracticeName ___________________________________________________Date _____________________1. What are the solutions of the quadratic equation x 2 5x 6?a. –3, –2b. 2, 3c. –2, 3d. –3, 22. Which expression is a solution of the equation 3x 2 5x 1 0?a.b.c.d.5 1365 3765 1365 37633. The value of the discriminant for a quadratic equation is 18. What does this value tell youabout the solution(s) of the quadratic equation?a. There are no real solutions.b. There is 1 real solution.© 2008 Carnegie Learning, Inc.c. There are 2 real solutions.d. None of the above.Georgia Mathematics 1 Chapter 3 ■ Assessments 243

Standardized Test Practice PAGE 24. The graph of the equation y x 2 2x 8 is shown below.y87654321−8 −7 −6 −5 −4 −3 −1 O 1 2 3 5 6 7 8−1x3−2−3−4−5−6y = x 2 − 2x − 8−8For what value(s) of x is y 0?a. x 2 onlyb. x 4 onlyc. x 4 and 2d. x 2 and 45. How many x-intercepts does the graph of y 3x 2 have?a. noneb. one© 2008 Carnegie Learning, Inc.c. twod. three244 Chapter 3 ■ Assessments Georgia Mathematics 1

Standardized Test Practice PAGE 3Name ___________________________________________________Date _____________________6. You can model the height in feet of a toy rocket that is launched from the ground by usingthe equation y 16t 2 100t 1.5,where t is the time the rocket has been moving inseconds. What is the height of the rocket 3 seconds after it is launched?a. 157.5 feetb. 253.5 feetc. 300 feetd. 445.5 feet7. Janine and Zachary each put a fence around their square yards. Zachary’s yard isthree times as long and three times as wide as Janine’s yard. The area of Janine’syard is 900 square feet. What is the area of Zachary’s yard?a. 810 square feetb. 2700 square feetc. 8100 square feet3d. cannot be determined8. Ataysha’s bedroom is a square with a floor space that is 144 square feet.How can Ataysha best determine the length of each side of her floor?a. Divide 144 by 4.b. Take the square root of 144.c. Multiply 144 by 4.© 2008 Carnegie Learning, Inc.d. Take the square root of 144 and multiply it by 4.Georgia Mathematics 1 Chapter 3 ■ Assessments 245

Standardized Test Practice PAGE 49. Which graph shows the graph of the equation y 3x 2 6x 4?a. yb.1y1−4 −3 −2 −1 O 1 2 3 4x−4 −3 −2 −1 O 1 2 3 4x−1−1−2−2−3−3−4−4−5−5−73c. yd.1y1−4 −3 −2 −1 O 1 2 3 4x−4 −3 −2 −1 O 1 2 3 4x−1−1−2−2−3−3−4−4−5−6−710. What is the line of symmetry of the graph of the equation y 6x 2 4x 9?a.b.x 3x 3© 2008 Carnegie Learning, Inc.c.x 1 3d. x 1 3246 Chapter 3 ■ Assessments Georgia Mathematics 1

Standardized Test Practice PAGE 5Name ___________________________________________________Date _____________________11. What is the vertex of the graph of the equation y x 2 4x 5?a. (1, 2)b. (2, 1)c. (–2, 17)d. (17, –2)12. Which way does the graph of the equation y 1 open?6 x2a. upb. downc. leftd. right313. What is the value of the function h(x) 26 2x 2 at x 3?a.b.c.h(3) 8h(3) 20h(3) 32d. h(3) 44© 2008 Carnegie Learning, Inc.Georgia Mathematics 1 Chapter 3 ■ Assessments 247

Standardized Test Practice PAGE 614. What do the x-intercepts in the graph below represent?7.57.06.56.05.55.0yFlea Jump3Height (inches)4.54.03.53.02.52.01.51.00.50.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Horizontal distance (inches)xa. The height of the flea in the middle of the jump.b. The speed of the flea.c. The path of the flea.d. The starting and landing points of the flea.15. What is the value of 21 rounded to the nearest tenth?a. 4.4b. 4.5c. 4.6© 2008 Carnegie Learning, Inc.d. 4.7248 Chapter 3 ■ Assessments Georgia Mathematics 1

Pre-TestName ___________________________________________________Date _____________________Identify the values of a, b, and c in each quadratic function.1. y 2x 2 4x 62.y 15 x 2a = 2, b = –4, c = –6 a = –1, b = 0, c = 15Evaluate each quadratic function for the given value of x. Show all your work.3. f(x) 2x 2 3x 5; f(4)4.g(x) 4x 2 7x; g(2)f(4) = 2(4) 2 – 3(4) + 5 g(–2) = –4(–2) 2 + 7(–2)= 2(16) – 12 + 5 = –4(4) – 14= 32 – 12 + 5 = –16 – 14= 25 = –305. Complete the table of values for the given quadratic function.3y 1 8 x2x–16–8–40y32820© 2008 Carnegie Learning, Inc.48162832Georgia Mathematics 1 Chapter 3 ■ Assessments 225

Pre-Test PAGE 26. Create a graph of the quadratic function in Question 5 on the grid below. First chooseyour bounds and intervals. Be sure to label your graph clearly.Answers may vary. A sample answer has been provided below.Variable quantity Lower bound Upper bound Intervalxy–18 18 2–8 64 4y60565234844408363228241y = x8220161284−16 −14 −12 −10 −8 −6 −4 −2 O 2 4 6 8 10 12 14 16−47. Identify the domain and range of the quadratic function that you graphed in Question 6.The domain is all real numbers, and the range is all positive real numbers.x© 2008 Carnegie Learning, Inc.226 Chapter 3 ■ Assessments Georgia Mathematics 1

Pre-Test PAGE 3Name ___________________________________________________Date _____________________8. Write the equation of the line of symmetry for the parabola given by the equationy x 2 6x 14. Show all your work and use a complete sentence in your answer.x b2a 62(1) 623The line of symmetry is x 3.Find the vertex of the graph of each quadratic function. Then tell whether they-coordinate of the vertex is a minimum or a maximum. Show all your workand use a complete sentence in your answer.9. y 3x 2 24x 710.y 4x 2 323x 242(3) 246 4y 3(4) 2 24(4) 7y 48 96 7y 55The vertex is (–4, 55), and it is a maximum.x 02(4) 0y 4(0) 2 32y 0 32y 32The vertex is (0, 32), and it is a minimum.© 2008 Carnegie Learning, Inc.Complete each statement.11. 64 8 12. 16 –413. Approximate 42 to the nearest tenth. Show all your work.36 < 42 < 4936 < 42 < 496 < 42 < 76.5 2 42.2542 ≈ 6.5Georgia Mathematics 1 Chapter 3 ■ Assessments 227

Pre-Test PAGE 414. What x-values do you think will be zeroes of the given quadratic equation?Use complete sentences to explain your reasoning.y 1.25(x 2)(x 2)Sample Answer: The solutions are 2 and –2, because when x = 2, then (x – 2) = 0 andzero multiplied by any number is zero. Likewise, when x = –2, then (x + 2) = 0 and zeromultiplied by any number is zero.15. What x-values do you think will be solutions to the given quadratic equation?Write your solutions in radical form if necessary. Use a complete sentence in your answer.x 2 120Sample Answer: The solutions to the equation are 120 and 120 .316. Find the zeroes of the quadratic function by using the Quadratic Formula. Show all your work.y 6x 2 7x 2a 6, b 7, c 2x 772 4(6)(2)2(6)749 4812 7 112So, the solutions are x 7 1 6 and x 7 1 8 .12 12 1 212 12 2 317. What does the value of the discriminant tell you about the number of solutions to aquadratic equation? Use complete sentences in your answer.Sample Answer: When the discriminant is positive, there are two solutions. When thediscriminant is zero, there is one solution. When the discriminant is negative, there areno solutions.© 2008 Carnegie Learning, Inc.18. Suppose that a ball is thrown straight up into the air from a height of 5 feet at an initialvelocity of 15 feet per second. Write a quadratic function that models the height of theball in terms of time using the vertical motion model y 16t 2 vt h.y 16t 2 15t 5228 Chapter 3 ■ Assessments Georgia Mathematics 1

Post-TestName ___________________________________________________Date _____________________Identify the values of a, b, and c in each quadratic function.1. y x 2 3x 92.y 24 2x 2a = 1, b = –3, c = 9 a = –2, b = 0, c = 24Evaluate each quadratic function for the given value of x. Show all your work.3. f(x) 5x 2 2x 18; f(3)4.g(x) 6x 2 8x; g(3)f(3) = 5(3) 2 + 2(3) + 18 g(–3) = –6(–3) 2 – 8(–3)= 5(9) + 6 + 18 = –6(9) + 24= 45 + 6 + 18 = –54 + 24= 69 = –305. Complete the table of values for the given quadratic function.3y 1 9 x2x–9–6–30y9410© 2008 Carnegie Learning, Inc.369149Georgia Mathematics 1 Chapter 3 ■ Assessments 229

Post-Test PAGE 26. Create a graph of the quadratic function in Question 5 on the grid below. First chooseyour bounds and intervals. Be sure to label your graph clearly.Answers may vary. A sample answer has been provided below.Variable quantity Lower bound Upper bound Intervalxy–9 9 1–4 14 1y13121131098761y = x9254321−8 −7 −6 −5 −4 −3 −2 −1 O 1 2 3 4 5 6 7 8−1−2−37. Identify the domain and range of the quadratic function that you graphed in Question 6.The domain is all real numbers, and the range is all positive real numbers.x© 2008 Carnegie Learning, Inc.230 Chapter 3 ■ Assessments Georgia Mathematics 1

Post-Test PAGE 3Name ___________________________________________________Date _____________________8. Write the equation of the line of symmetry for the parabola given by the equationy 2x 2 16x 10. Show all your work and use a complete sentence in your answer.x b2a 162(2) 1644The line of symmetry is x 4.Find the vertex of the graph of each quadratic function. Then tell whether they-coordinate of the vertex is a minimum or a maximum. Show all your workand use a complete sentence in your answer.9. y x 2 6x 810.y 3x 2 153x –62(1) 62 3y (3) 2 6(3) 8y 9 18 8y 1The vertex is (3, 1), and it is a maximum.x 02(3) 0y 3(0) 2 15y 0 15y 15The vertex is (0, –15), and it is a minimum.© 2008 Carnegie Learning, Inc.Complete each statement.11. 36 6 12. 121 –1113. Approximate 55 to the nearest tenth. Show all your work.49 < 55 < 6449 < 55 < 647 < 55 < 87.5 2 56.257.4 2 54.7655 ≈ 7.4Georgia Mathematics 1 Chapter 3 ■ Assessments 231

Post-Test PAGE 414. What x-values do you think will be zeroes of the given quadratic equation?Use complete sentences to explain your reasoning.y 3.5(x 6)(x 6)Sample Answer: The solutions are 6 and –6, because when x = 6, then (x – 6) = 0 andzero multiplied by any number is zero. Likewise, when x = –6, then (x + 6) = 0 and zeromultiplied by any number is zero.15. What x-values do you think will be solutions to the given quadratic equation?Write your solutions in radical form if necessary. Use a complete sentence in your answer.x 2 115Sample Answer: The solutions to the equation are 115 and 115 .316. Find the zeroes of the quadratic function using the Quadratic Formula. Show all your work.y 8x 2 9x 1a 8, b 9, c 1x 992 4(8)(1)2(8) 94916 9 716So, the solutions are x 9 7 2 and x 9 7 16 .16 16 1 816 16 117. What does the value of the discriminant tell you about the number of solutions to aquadratic equation? Use complete sentences in your answer.Sample Answer: When the discriminant is positive, there are two solutions. When thediscriminant is zero, there is one solution. When the discriminant is negative, there areno solutions.© 2008 Carnegie Learning, Inc.18. Suppose that a ball is thrown straight up into the air from a height of 6 feet at an initialvelocity of 18 feet per second. Write a quadratic function that models the height of theball in terms of time using the vertical motion model y 16t 2 vt h.y 16t 2 18t 6232 Chapter 3 ■ Assessments Georgia Mathematics 1

Mid-Chapter TestName ___________________________________________________Date _____________________Evaluate each quadratic function for the given value of x. Show all your work.1. g(x) 5x 2 3x 28; g(6)2.h(x) 48 2x 2 ; f(5)g(6) = –5(6) 2 + 3(6) – 28 h(–5) = 48 – 2(–5) 2= –5(36) + 18 – 28 = 48 – 2(25)= –180 + 18 – 28 = 48 – 50= –190 = –2Read the scenario below. Use the scenario to answer Questions 3 through 6.The jump of a cricket can be modeled by the function y 3x 2 6x, where x is the horizontaldistance the cricket moves in feet and y is the height of the cricket’s jump in feet.3. Complete the table of values that shows the height of the cricket’s jump as a function ofthe horizontal distance.3LabelsUnitsExpressionsHorizontal distancefeetx00.511.5Heightfeet3x 2 6x02.2532.25© 2008 Carnegie Learning, Inc.20Georgia Mathematics 1 Chapter 3 ■ Assessments 233

Mid-Chapter Test PAGE 24. Create a graph of the quadratic function on the grid below. First, choose your bounds andintervals. Be sure to label your graph clearly.Answers may vary. Sample answers are provided below.Variable quantity Lower bound Upper bound IntervalHorizontal distance 0 3.75 0.25Height 0 3.75 0.253.753.503.25yA Cricket’s Jump33.002.752.50Height (feet)2.252.001.751.501.251.000.750.500.25y = −3x 2 + 6x0.00x0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75Horizontal distance (feet)5. What is the domain and range of the function in the problem situation? Use a completesentence in your answer.The domain is zero to two and the range is zero to three.© 2008 Carnegie Learning, Inc.6. Determine the x-intercepts of the graph. Interpret the meaning of the x-intercepts in theproblem situation. Use complete sentences in your answer.Sample Answer: The x-intercepts are 0 and 2. The x-intercepts indicate the startingand landing points for the cricket. The intercept (2, 0) gives the horizontal distance thecricket jumped.234 Chapter 3 ■ Assessments Georgia Mathematics 1

Mid-Chapter Test PAGE 3Name ___________________________________________________Date _____________________Use the quadratic function y = –2x 2 – 4x – 3 for Questions 7 through 9.7. Algebraically determine the line of symmetry and the vertex of the graph. Show all yourwork and use a complete sentence in your answer.x 42(2)4 41y 2(1) 2 4(1) 32 4 31The axis of symmetry is x = –1 and the vertex is (–1, –1).38. Draw the graph of the function. Be sure to graph and label the line of symmetry andthe vertex.y87x = −16543© 2008 Carnegie Learning, Inc.21−8 −7 −6 −5 −4 −3 −2 O 1 2 3 4 5 6 7 8(−1, −1)−1−3−4y = −2x 2 − 4x − 3x−5−6−7−8Georgia Mathematics 1 Chapter 3 ■ Assessments 235

Mid-Chapter Test PAGE 49. What is the domain and range of the quadratic function? Use a complete sentence inyour answer.The domain is all real numbers and the range is all real numbers less than or equal to –1.Determine whether the vertex of the given quadratic function is a maximum or aminimum. Use a complete sentence to explain your reasoning.10.y 15x 2 2x 29Sample Answer: The coefficient of the squared term is negative, so, the parabola opensdownward and the vertex is the maximum.11.y 8x 2 17x 543Sample Answer: The coefficient of the squared term is positive, so, the parabola opensupward and the vertex is the minimum.Complete each statement below.12. 144 12 13. 49 –714. Approximate 77 to the nearest tenth. Show all your work.64 < 77 < 8164 < 77 < 818 < 77 < 98.5 2 72.258.7 2 75.698.8 2 77.4477 ≈ 8.8© 2008 Carnegie Learning, Inc.236 Chapter 3 ■ Assessments Georgia Mathematics 1

End of Chapter TestName ___________________________________________________Date _____________________Read the scenario below. Use the scenario to answer Questions 1 through 7.The path of a diver in the water can be modeled by the function y 0.16x 2 3.2x, where x isthe horizontal distance in feet that the diver travels and y is the depth in feet of the diver.1. Complete that table of values that shows the depth as a function of the horizontal distance.LabelsUnitsHorizontal distancefeetDepthfeetExpressionsx 0.16x 2 3.2x051015200–12–16–12032. Write the equation of the line of symmetry. Show all your work and use a completesentence in your answer.x 3.22(0.16) 3.20.32 10The axis of symmetry is x = 10.© 2008 Carnegie Learning, Inc.3. Find the vertex of the graph of the function. Show all your work and use a completesentence in your answer.y = 0.16(10) 2 – 3.2(10)= 0.16(100) – 32= 16 – 32= –16The vertex is (10, –16).Georgia Mathematics 1 Chapter 3 ■ Assessments 237

End of Chapter Test PAGE 24. Create a graph of the quadratic function that models the diver’s path on the grid below.First, choose your bounds and intervals. Be sure to label your graph clearly including theline of symmetry and the vertex.Answers may vary. Sample answers are provided below.Variable quantity Lower bound Upper bound IntervalHorizontal distance –2 28 2Depth –28 2 2yA Diver’s Path3−2 2 4 6 8 12 14 16 18 22 24−2−4−6−8xDepth (feet)−10−12−14−16−18(10, −16)y = 0.16x 2 − 3.2x−20−22x = 10−24−26Horizontal distance (feet)5. What is the domain and range of the function in terms of the problem situation?Use complete sentences in your answer.Sample Answer: The domain is all real numbers from 0 to 20, and the range is all realnumbers from 0 to –16.© 2008 Carnegie Learning, Inc.6. Determine the x-intercepts of the graph. Interpret the meaning of the x-intercepts in theproblem situation. Use complete sentences in your answer.Sample Answer: The x-intercepts are 0 and 20. The intercepts indicate the points wherethe diver enters and exits the water. The intercept (20, 0) gives the horizontal distance thediver travels.238 Chapter 3 ■ Assessments Georgia Mathematics 1

End of Chapter Test PAGE 3Name ___________________________________________________Date _____________________7. How deep is the diver at a horizontal distance of 8 feet? Show all your work and use acomplete sentence in your answer.y = 0.16(8) 2 – 3.2(8)= 0.16(64) – 25.6= 10.24 – 25.6= –15.36The diver is 15.36 feet deep.Determine whether the vertex of the given quadratic function is a maximum or aminimum. Use a complete sentence to explain your reasoning.8.y 7x 2 9x 10Sample Answer: The coefficient of the squared term is positive, so, the parabola opensupward and the vertex is the minimum.39.y 18 6x 2Sample Answer: The coefficient of the squared term is negative, so, the parabola opensdownward and the vertex is the maximum.10. Approximate 11 to the nearest tenth. Show all your work.© 2008 Carnegie Learning, Inc.9 < 11 < 169 < 11 < 163 < 11 < 43.5 2 12.253.4 2 11.563.3 2 10.8911 ≈ 3.3Georgia Mathematics 1 Chapter 3 ■ Assessments 239

End of Chapter Test PAGE 4Read the scenario below. Use the scenario to answer Questions 11 through 15.Tanya’s jump rope forms the shape of a parabola as she jumps. The shape can be modeled bythe equation y 2 (x 3)(x 3) , where x is the number of feet to the right of Tanya’s waist,3and y is the height of the jump rope above Tanya’s waist as she swings the rope over her head.11. Create a graph of the quadratic function on the grid below. First, choose your bounds andintervals. Be sure to label your graph clearly.Answers may vary. Sample answers are provided below.Variable quantity Lower bound Upper bound Interval3Horizontal distanceHeight–3.5 4.0 0.5–1.0 6.5 0.5Jumping Ropey5.55.0y = − 2 (x + 3)(x − 3)34.54.0Height (feet)3.53.02.52.01.51.00.5−3.0 −2.5 −2.0 −1.5 −1.0 −0.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5−0.5Horizontal distance (feet)x© 2008 Carnegie Learning, Inc.12. What is the y-intercept of the graph? What does it represent in the problem situation?Use complete sentences in your answer.Sample Answer: The y-intercept is 6. It is the height of the jump rope above Tanya’s waist,as she swings the rope over her head.240 Chapter 3 ■ Assessments Georgia Mathematics 1

End of Chapter Test PAGE 5Name ___________________________________________________Date _____________________13. What are the x-intercepts of the graph? What do they represent in the problem situation?Use complete sentences in your answer.The x-intercepts are –3 and 3. They represent the horizontal position of the ends of thejump rope which are level with Tanya’s waist.14. What is the horizontal distance between the ends of the jump rope? Use a complete sentencein your answer.The horizontal distance between the ends of the jump rope is 6 feet.15. What are the zeroes of this function? Use complete sentences to explain your reasoning.The solutions to the equation are –3 and 3, because when x = –3, then (x + 3) = 0 and zeromultiplied by any number is zero. When x = 3, then (x – 3) = 0 and zero multiplied by anynumber is zero.316. What are the solutions to the equation x 2 95? Give your answers in radical form, anduse a complete sentence in your answer.The solutions are 95 and 95.Use the following scenario for Questions 17 through 20.© 2008 Carnegie Learning, Inc.Jude builds a water balloon launcher that launches the balloon straight up. The motion of aballoon that is released by the launcher can be modeled by using the vertical motion modely 16t 2 vt h, where t is the time that the object has been moving in seconds, v isthe initial velocity of the object in feet per second, h is the initial height of the object in feet,and y is the height of the object in feet at time t seconds.17. The launcher is designed to launch the water balloon from a height of 2.75 feet at aninitial velocity of 20 feet per second. Write a quadratic function that models the heightof the water balloon in terms of time.y 16t 2 20t 2.75Georgia Mathematics 1 Chapter 3 ■ Assessments 241

End of Chapter Test PAGE 618. Identify a, b, and c, and then find the zeroes of the quadratic function using the QuadraticFormula. Show all your work and use a complete sentence in your answer.y 16t 2 20t 2.75a 16, b 20, c 2.75t 20202 4(16)(2.75)2(16)20400 17632 2057632320 243220 2420 24So, the solutions are t 4 and t 44.32 32 1132 32 1 88 or 13 819. Would the zeroes have meaning in the problem situation? Use a complete sentencein your answer.Sample Answer: No, the solutionnegative time. 1 8doesn’t make sense, because you can’t have20. What is the height of the balloon 0.5 second after launch? Show all your work and use acomplete sentence in your answer.y = –16(0.5) 2 + 20(0.5) + 2.75y = –4 + 10 + 2.75y = 8.75The height of the balloon 0.5 second after launch is 8.75 feet.21. What is the discriminant? How does it help you determine the number of solutions to aquadratic equation? Use complete sentences in your answer.© 2008 Carnegie Learning, Inc.The discriminant is the expression b 2 – 4ac. If it is positive, then there are two solutions.If it is zero, then there is one solution. If it is negative, then there are no solutions.242 Chapter 3 ■ Assessments Georgia Mathematics 1

Standardized Test PracticeName ___________________________________________________Date _____________________1. What are the solutions of the quadratic equation x 2 5x 6?a. –3, –2b. 2, 3c. –2, 3d. –3, 22. Which expression is a solution of the equation 3x 2 5x 1 0?a.b.c.d.5 1365 3765 1365 37633. The value of the discriminant for a quadratic equation is 18. What does this value tell youabout the solution(s) of the quadratic equation?a. There are no real solutions.b. There is 1 real solution.© 2008 Carnegie Learning, Inc.c. There are 2 real solutions.d. None of the above.Georgia Mathematics 1 Chapter 3 ■ Assessments 243

Standardized Test Practice PAGE 24. The graph of the equation y x 2 2x 8 is shown below.y87654321−8 −7 −6 −5 −4 −3 −1 O 1 2 3 5 6 7 8−1x3−2−3−4−5−6y = x 2 − 2x − 8−8For what value(s) of x is y 0?a. x 2 onlyb. x 4 onlyc. x 4 and 2d. x 2 and 45. How many x-intercepts does the graph of y 3x 2 have?a. noneb. one© 2008 Carnegie Learning, Inc.c. twod. three244 Chapter 3 ■ Assessments Georgia Mathematics 1

Standardized Test Practice PAGE 3Name ___________________________________________________Date _____________________6. You can model the height in feet of a toy rocket that is launched from the ground by usingthe equation y 16t 2 100t 1.5,where t is the time the rocket has been moving inseconds. What is the height of the rocket 3 seconds after it is launched?a. 157.5 feetb. 253.5 feetc. 300 feetd. 445.5 feet7. Janine and Zachary each put a fence around their square yards. Zachary’s yard isthree times as long and three times as wide as Janine’s yard. The area of Janine’syard is 900 square feet. What is the area of Zachary’s yard?a. 810 square feetb. 2700 square feetc. 8100 square feet3d. cannot be determined8. Ataysha’s bedroom is a square with a floor space that is 144 square feet.How can Ataysha best determine the length of each side of her floor?a. Divide 144 by 4.b. Take the square root of 144.c. Multiply 144 by 4.© 2008 Carnegie Learning, Inc.d. Take the square root of 144 and multiply it by 4.Georgia Mathematics 1 Chapter 3 ■ Assessments 245

Standardized Test Practice PAGE 49. Which graph shows the graph of the equation y 3x 2 6x 4?a. yb.1y1−4 −3 −2 −1 O 1 2 3 4x−4 −3 −2 −1 O 1 2 3 4x−1−1−2−2−3−3−4−4−5−5−73c. yd.1y1−4 −3 −2 −1 O 1 2 3 4x−4 −3 −2 −1 O 1 2 3 4x−1−1−2−2−3−3−4−4−5−6−710. What is the line of symmetry of the graph of the equation y 6x 2 4x 9?a.b.x 3x 3© 2008 Carnegie Learning, Inc.c.x 1 3d. x 1 3246 Chapter 3 ■ Assessments Georgia Mathematics 1

Standardized Test Practice PAGE 614. What do the x-intercepts in the graph below represent?7.57.06.56.05.55.0yFlea Jump3Height (inches)4.54.03.53.02.52.01.51.00.50.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Horizontal distance (inches)xa. The height of the flea in the middle of the jump.b. The speed of the flea.c. The path of the flea.d. The starting and landing points of the flea.15. What is the value of 21 rounded to the nearest tenth?a. 4.4b. 4.5c. 4.6© 2008 Carnegie Learning, Inc.d. 4.7248 Chapter 3 ■ Assessments Georgia Mathematics 1

AssignmentAssignment for Lesson 3.1Name ___________________________________________________Date _____________________Website DesignIntroduction to Quadratic FunctionsIdentify the values of a, b, and c in each quadratic function.1. y 2x 2 3x 12. y 3x 2 5x3.y x 2 4x 2a = 2, b = 3, c = –1 a = 3, b = –5, c = 0 a = 1, b = 4, c = 2Evaluate each quadratic function for the given value of x. Show all your work.4. f(x) 2x 2 3x 1; f(2) 5. f(x) 3x 2 5x; f(1)6.f(x) x 2 4x; f(0)f(2) = 2(2) 2 + 3(2) – 1 f(–1) = 3(–1) 2 – 5(–1) f(0) = (0) 2 + 4(0)= 8 + 6 –1 = 3 + 5 = 0 + 0= 13 = 8 = 03As the set designer for your school play, you have to build an archway for one of the scenes.The archway needs to be 14 feet wide and 12 feet high. Before cutting the archway in a pieceof plywood, you draw a plan on a coordinate grid. The table below shows some of the pointson the archway with respect to the origin. The origin represents the lower left-hand corner ofthe plywood sheet where you will begin cutting.LabelsUnitsHorizontal distancefeetVertical distancefeet© 2008 Carnegie Learning, Inc.0 05 11.027 129 11.0214 07. Create a scatter plot of the points on the archway on the grid. First, choose your boundsand intervals. Be sure to label your graph clearly.Variable quantity Lower bound Upper bound IntervalHorizontal distance 0 15 1Vertical distance 0 15 1Georgia Mathematics 1 Chapter 3 ■ Assignments 127

1514131211yArchwayVertical distance (feet)10987654332100 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15x8. Connect the points with a smooth curve to create the drawing of the archway.© 2008 Carnegie Learning, Inc.Horizontal distance (feet)128 Chapter 3 ■ Assignments Georgia Mathematics 1

AssignmentAssignment for Lesson 3.2Name ___________________________________________________Date _____________________Satellite DishParabolasDefine each term in your own words.1. parabolaThe U-shaped graph a quadratic function2. vertexThe highest or lowest point of a parabola3. line of symmetryThe vertical line that divides a parabola so that the graph in one sideof the line is a mirror image of the graph on the other side of the lineFor each function, algebraically determine the vertex and the line of symmetryof the graph. Then draw the graph for each function. Identify the domain andrange for each function.4. y x 2 3 x = 0 = 0; y = (0) 2 + 3 = 3; Vertex: (0, 3); Line of symmetry: x = 0;2(1)Domain: All real numbers; Range: All real numbers greater than or equal to 33y14131211y = x 2 + 3© 2008 Carnegie Learning, Inc.1098765421−8 −7 −6 −5 −4 −3 −2 −1 O 1 2 3 4 5 6 7 8−1x−2Georgia Mathematics 1 Chapter 3 ■ Assignments 129

5. y x 2 3x 5x 32(1) 1.5;y ( 3 2) 2 3 ( 3 2) 5 9 4 9 2 5 7.25Vertex: (1.5, 7.25); Line of symmetry: x = 1.5; Domain: All real numbers;Range: All real numbers less than or equal to 7.25y1110983765y = −x 2 + 3x + 521−8 −7 −6 −5 −4 −3 −2 −1 O 1 2 3 4 5 6 7 8−1x−2−3−4−5© 2008 Carnegie Learning, Inc.130 Chapter 3 ■ Assignments Georgia Mathematics 1