Chapter 4 Extra Practice Answers
- 1. Name Class Date Extra Practice Chapter 4 Lessons 4-1 and 4-2 Graph each system. 1. y 5 3x 2 2. y 5 (x 1 3)2 1 1 3. y 5 2x 2 1 4 y y y 4 4 6 2 2 x x 2 -4 -2 O 2 4 -4 -2 O 2 x -2 -2 -4 -2 O 2 4 4. y 5 (x 1 1)2 2 3 5. y 5 (x 2 2)2 6. y 5 22(x 2 1)2 1 3 y y y 4 4 2 2 2 x x -2 O 2 4 -4 -2 O 2 x -2 O 2 4 -2 -2 -2 -4 -4 Identify the vertex, axis of symmetry, minimum or maximum value, and domain and range of each function. 1 7. y 5 4(x 2 2)2 8. f (x) 5 (x 1 1)2 1 2 9. y 5 22(x 2 4)2 2 10 (2, 0); x 5 2; minimum: 0; (21, 2); x 5 21; minimum: (4, 22); x 5 4; maximum: domain: all real numbers; 2; domain: all real numbers; 22; domain: all real range: y $ 0 range: f (x) $ 2 numbers; range: y # 22 10. f (x) 5 x 2 2 4x 1 5 11. f (x) 5 22x 2 1 4x 2 3 12. y 5 x 2 1 5x 2 14 (2, 1); x 5 2; minimum: 1; (1, 21); x 5 1; maximum:21; Q 25, 281 R ; x 5 25 ; minimum: 2 4 2 domain: all real numbers; domain: all real numbers; range: y $ 1 range: y # 21 281 ; domain: all real numbers; 4 range: y $ 281 4 13. A ball is dropped from the top of a building. The distance in meters above the ground y of the ball after t seconds can be modeled by the equation y 5 29.8t 2 1 100. a. What is the y-intercept of the equation? 100 The y-intercept is the starting b. Describe the meaning of the y-intercept of the graph of the equation. height of the ball. Prentice Hall Algebra 2 • Extra Practice Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 13
- 2. Name Class Date Extra Practice (continued) Chapter 4 14. Martin has 120 feet of fencing to enclose two rectangular play areas for children. He plans to enclose a rectangular area and then divide it into two equal sections, as shown in the figure. a. Find the dimensions of the largest total area Martin can enclose. 30 ft by 20 ft b. Find the area of each of the small play areas. 300 ft 2 15. Marnie throws a softball straight up into the air. The ball leaves her hand when it is exactly 5 ft from the ground. The height h of the ball, in feet, can be written as a function of time t, in seconds, as h 5 216t 2 1 40t 1 5. a. What is the maximum height the ball reaches? 30 ft b. Marnie catches the ball 5 ft from the ground. How long was the ball in the air? 2.5 s Lesson 4-3 Find an equation in standard form of the parabola passing through the given points. 16. (0, 3), (1, 2), (2, 3) 17. (23, 24), (0, 24), (1, 0) 18. (21, 0), (0, 3), (1, 2) y 5 x 2 2 2x 1 3 y 5 x 2 1 3x 2 4 y 5 22x2 1 x 1 3 19. (24, 3), (22, 21), (2, 3) 20. (0, 0), (1,23), (2, 2) 21. (23, 0), (0, 23), (3, 0) y5 1 2 1x21 y 5 4x 2 2 7x y 5 21x 2 1 3 2x 3 22. The table shows the relation between the Speed (mi/h) 35 45 50 60 speed of a car and its stopping distance. Stopping Distance (ft) 96 140 165 221 a. Use a quadratic function to model the data. f(x) 5 0.04x 2 1 1.2x 1 5 b. Predict the stopping distance for a car traveling at 65 mi/h. 252 ft Lesson 4-4 Factor each expression. 23. x 2 1 3x 2 54 24. x 2 1 10x 1 24 25. x 2 2 36 (x 1 9)(x 2 6) (x 1 6)(x 1 4) (x 2 6)(x 1 6) 26. x 2 2 9x 2 36 27. x 2 2 15x 1 56 28. 25x 2 1 70x 1 49 (x 2 12)(x 1 3) (x 2 8)(x 2 7) (5x 1 7)2 1 29. 7x 2 2 20x 2 3 30. 5x 2 1 23x 2 10 31. 4 x 2 2 4 (7x 1 1)(x 2 3) (5x 2 2)(x 1 5) 1 4 (x 2 4)(x 1 4) 32. x 2 2 6x 2 16 33. 4x 2 1 12x 1 40 34. 4x 2 2 6x 1 9 (x 2 8)(x 1 2) 4(x2 1 3x 1 10) cannot be factored Prentice Hall Algebra 2 • Extra Practice Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 14
- 3. Name Class Date Extra Practice (continued) Chapter 4 Lesson 4-5 Solve each equation by factoring, by taking square roots, or by graphing. When necessary, round your answer to the nearest hundredth. 35. x 2 1 4x 2 1 5 0 36. 4x 2 2 100 5 0 37. x 2 5 22x 1 1 0.24, 24.24 45 0.41, 22.41 38. x 2 2 9 5 0 39. 2x 2 1 4x 5 70 40. x 2 2 30 5 10 43 27, 5 46.32 41. x 2 1 4x 5 0 42. x 2 1 3x 1 2 5 0 43. x 2 1 8x 5 216 0, 24 22, 21 24 44. Hal’s sister is 5 years older than Hal. The product of their ages is 456. How old are Hal and his sister? 19 years old; 24 years old 45. A toy rocket is fired upward from the ground. The relation between its height h, in feet, and the time t from launch, in seconds, can be described by the equation h 5 216t 2 1 64t . How long does the rocket stay more than 48 feet above the ground? 2 s 46. The expression P(x) 5 2500x 2 2x 2 describes the profit of a company that customizes bulldozers when it customizes x bulldozers in a month. a. How many bulldozers per month must the company customize to make the maximum possible profit? What is the maximum profit? 625 bulldozers; $781,250 b. Describe a reasonable domain and range for the function P (x). x $ 0; P(x) # $ 781,250 c. For what number of bulldozers per month is the profit at least $750,000? 500 # x # 750 47. Flor is designing a kite with two perpendicular crosspieces that are B 26 inches and 24 inches long, as shown in the figure. How long should AK be so that AB ' BC and AD ' DC? 8 in. K 24 in. A 48. The lengths of the sides of a right triangle are x, x 1 4, and C x 1 8 inches. What is the value of x? What is the length of D 26 in. the hypotenuse of the triangle? 12; 20 in. Lessons 4-6 and 4-7 Solve each equation by completing the square or using the Quadratic Formula. 49. x 2 1 5x 1 8 5 4 21, 24 50. 2x 2 2 5x 1 1 5 0 51. x 2 2 7x 5 0 0, 7 5 "17 4 4 4 52. x 2 1 4x 1 4 5 0 53. x 2 2 7 5 0 54. x 2 1 8x 2 17 5 0 22 4"7 24 4 "33 Prentice Hall Algebra 2 • Extra Practice Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 15
- 4. Name Class Date Extra Practice (continued) Chapter 4 Evaluate the discriminant of each equation. Tell how many real solutions each equation has. 55. x 2 1 4x 5 17 84; 2 56. 2x 2 1 x 5 21 27; 0 57. x 2 2 4x 1 5 5 0 24; 0 58. 2x 2 1 5x 5 0 25; 2 59. x 2 2 19 5 1 80; 2 60. 3x 2 5 8x 2 4 16; 2 61. 22x 2 1 1 5 7x 57; 2 62. 4x 2 1 4x 5 21 0; 1 63. x 2 1 16 5 0 264; 0 1 64. The height y of a parabolic arch is given by y 5 216 x 2 1 40, where x is the horizontal distance from the center of the base of the arch. All distances are in feet. a. What is the highest point on the arch? 40 ft b. How wide is the arch at the base to the nearest tenth of a foot? 50.6 ft 65. An archer’s arrow follows a parabolic path. The path of the arrow can be described by the equation y 5 20.005x 2 1 2x 1 5. The archer releases the arrow 5 ft above a. Describe the meaning of the y-intercept of the graph of the equation. the ground. b. What is the horizontal distance the arrow travels before it hits the ground? Round your answer to the nearest foot. 402 ft Lesson 4-8 Simplify each number by using the imaginary number i. 66. "29 43i 67. "236 46i 68. "280 44i "5 69. "2289 417i 70. "2175 45i "7 71. "2117 43i "13 Simplify each expression. 72. (3 2 i) 1 (5 2 2i) 73. (4 1 2i)(1 2 i) 74. (4 1 2i) 2 (3 1 5i) 8 2 3i 6 2 2i 1 2 3i 75. (8 2 3i)(6 1 9i) 76. (2 1 5i) 2 (26 1 i) 77. (22 2 3i)(7 2 i) 75 1 54i 8 1 4i 217 2 19i Solve each equation. Check your answers. 78. x 2 1 16 5 0 44i 79. 3x 2 5 x 2 9 1 4 i "6 6 107 80. x 2 1 10 5 4x 2 2 2 4 2i "2 Lesson 4-9 Solve each system. y 5 x 2 2 11x 1 24 y 5 x 2 1 2x 2 8 y 5 2x 2 1 9x 2 5 81. e 82. e 83. e y 5 x 2 2 11x 2 23 y 5 x 2 1 2x 1 4 y 5 2x 2 1 9x 1 5 (3, 0), (9, 6) (24, 0), (3, 7) (25, 0), (1, 6) y5 2x 2 2 3x 2 7 y5 1x14 2x 2 y 5 x 2 2 2x 2 1 84. e 85. e 86. e 3 y 5 2x 2 2 3x 1 5 y 5 2x 2 2x 1 9 y 5 4x 2 1 x 2 6 5 71 (22, 3), (3, 27) Q 23 , 9 R , (1, 7) (2, 21), (10, 79) Prentice Hall Algebra 2 • Extra Practice Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 16