Name
Class
Date
Chapter 9
Extra Practice
Lesson 9-1
Without graphing, describe how each graph differs from the graph of y =x2.
1. y = 3x2 / 2.y =4x2 / 3.y = 0.5x24. y = 0.2x2 / 5.y =x2 4 / 6. y =x2 + 1
7. y = 2x2 + 5 / 8.y =0.3x2 7 / 9. y =5x2 + 0.8
10.Water from melting snow drips from a roof at a height of 40 ft. The function h =16t2 + 40 gives the approximate height h in feet of a drop of water t seconds after it falls. Graph the function.
Lesson 9-2
Identify the axis of symmetry and the vertex of each function.
11.y = 3x212.y =2x2 + 113.y = 0.5x2 3
14.y =x2 + 2x + 115. y = 3x2 + 6x16.
17.y = 2x2 918. y =5x2 + x + 419.y =x2 8x
Graph each quadratic equation.
20. y =x2 421. y = 2x2 + x22. y =x2 + x 2
The formula h =16t2 +vt +c describes the height of an object thrown into the air, where h is the height, t is the time in seconds, v is the initial velocity, and c is the initial height. Use the formula to answer each question.
23. A football is thrown with an upward velocity of 15 ft/s from an initial height of 5 feet. How long will it take for the football to reach its maximum height?
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Name
Class
Date
Chapter 9
Extra Practice(continued)
24. Aballisthrownfromthetopofa50-ftbuildingwithanupwardvelocityof24ft/s. When will it reach its maximum height? How far above the ground will it be?
Lessons 9-3 and 9-4
Solve each equation. If the equation has no solution, write no solution.
25.x2 = 36 / 26. x2 + x 2 = 0 / 27.c2 100 = 028.9d2 = 25 / 29.(x 4)2 = 100 / 30. 3x2 = 27
31.2x2 54 = 284 / 32.7n2 = 63 / 33.h2 + 4 = 0
Model each problem with a quadratic equation. Then solve. If necessary, round to the nearest tenth.
34.Findtheradiusofacircularlidwithanareaof12in.2.
35.Findthesidelengthofasquaresandboxwithanareaof150ft2.
36.Findthediameterofacircularpondwithanareaof300m2.
Answer each question by factoring a quadratic equation.
37.Thelengthofanopen-topboxis4cmlongerthanitswidth.Theboxwas made from a 480-cm2 rectangular sheet of material with 6 cm-by-6 cm squares cut from each corner. The height of the box is 6 cm. Find the dimensions of the box.
38.Supposeyouthrowarugbyballintotheairwithaninitialupwardvelocityof 29 ft/s and an initial height of 6 ft. The formula h =16t2 + 29t + 6 gives the ball’s height h in feet at time t seconds. Solve the equation for h = 0 to find when the ball will hit the ground.
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Name
Class
Date
Chapter 9
Extra Practice(continued)
Lessons 9-5 and 9-6
Solve each equation. If the equation has no solution, write no solution.
39. x2 + 6x 2 = 0 / 40. x2 5x = 7 / 41. x2 10x + 3 = 042.2x2 4x + 1 = 0 / 43.3x2 + x + 5 = 0 / 44.
45.x2 + 8x + 4 = 0 / 46.x2 2x 6 = 0 / 47.3x2 + x 7 = 0
48.x2 + 5x + 6 = 0 / 49. d2 144 = 0 / 50.c2 + 6 = 2 4c
51. x2 + 4x = 2x2x + 6 / 52. 3x2 + 2x 12 = x2 / 53.r2 + 4r + 1 = r
54. t2 3t 10 = 0 / 55. 3c2 + c 10 = c2 5 / 56.d2 + 2d + 10 = 2d + 100
Find the number of solutions of each equation.
57. 3x2 + 4x 7 = 0 / 58. 5x2 4x = 6 / 59. x2 20x + 101 = 160.2x2 8x + 9 = 4 / 61. 4x2 5x + 6 = 0 / 62. x2 2x + 7 = 0
63.Agriculture You are planting a rectangular garden. It is 5 feet longer than 3 times its width. The area of the garden is 250 ft2. Find the dimensions of the garden.
Solve by completing the square.
64.A rectangular patio has a length of x + 6 m, a width of x + 8 m, and a total area of 400 m2. Find the dimensions to the nearest tenth.
65.A tennis ball is hit with a vertical velocity of 40 ft/s from an initial height of 7 ft. In how many seconds will the ball hit the ground?
66.A ball is thrown from an initial height of 6 feet at a rate of 42 ft/s to someone standing on a roof 30 feet above the ground. Use the discriminant to determine if the ball will reach the person on the roof.
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Name
Class
Date
Chapter 9
Extra Practice(continued)
Lesson 9-7
Graph each set of data. Which model is most appropriate for each set?
67. (2,4),(4,4),(1,2),(5,1.5)68.(3,8),(4,6),(5,5),(6,4),(7,3)
69.(0,7),(1,3),(3,0.5),(2,1)
70.Useagraphingcalculatortodeterminewhat kind of function best models the data. Let t = 0 correspond to the year 2000. Write an equation that models the data.
Lesson 9-8
Solve each system of linear and quadratic equations. If the system has no solution, write no solution.
71.y = x2 + 9 / 72.y =x2 + x 3 / 73.y =x2 10y = 6x / y = 3x 5 / y = 3x
74.y =3x2 + x / 75.y =3x 18 / 76.y = 4x + 8
y =2x + 1 / y =x2 + 5x 2 / y =x2 + 7x 20
77.Thefollowingequationsmodelthenumberofbikessoldattwodifferentbike shops, where x is the number of months since the shops opened. In which month(s) did both shops sell the same number of bikes? How many bikes did each shop sell in those months?
Shop A: y =x2 + 40x
Shop B: y = 18x + 72
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