A-15 Answers to Selected Exercises 35. x y (–3, 4) –3 4 0 f(x) = – x2 – 3x – 1 2 1 2 21. x y 5 (c)(b) (a) (d) The graph of y = 1x - h22 is translated to the right h units if h is positive and to the left 0 h0 units if h is negative. 23. x y 2 4 0 f(x) = (x – 2)2 (a) 12, 02 (b) x = 2 (c) 1-∞, ∞2 (d) 30, ∞2 25. –4 –5 (–3, –4) 0 x y f(x) = (x + 3)2 – 4 (a) 1-3, -42 (b) x = -3 (c) 1-∞, ∞2 (d) 3-4, ∞2 27. (–1, –3) –6 3 0 x y f(x) = – (x + 1)2 – 3 1 2 (a) 1-1, -32 (b) x = -1 (c) 1-∞, ∞2 (d) 1-∞, -34 29. x f(x) = x2 – 2x + 3 (1, 2) 0 3 y (a) 11, 22 (b) x = 1 (c) 1-∞, ∞2 (d) 32, ∞2 31. x 0 y (5, –4) f(x) = x2 – 10x + 21 –4 5 (a) 15, -42 (b) x = 5 (c) 1-∞, ∞2 (d) 3-4, ∞2 33. x y (–3, 2) 2 –3 0 f(x) = –2x2 – 12x – 16 (a) 1-3, 22 (b) x = -3 (c) 1-∞, ∞2 (d) 1-∞, 24 (a) 1-3, 42 (b) x = -3 (c) 1-∞, ∞2 (d) 1-∞, 44 37. (a) 1-3, ∞2 (b) 1-∞, -32 39. (a) 1-∞, 22 (b) 12, ∞2 41. (a) 12, ∞2 (b) 1-∞, 22 43. (a) 1-∞, -22 (b) 1-2, ∞2 45. E 47. D 49. C 51. ƒ1x2 = 1 4 1x - 222 - 1, or ƒ1x2 = 1 4 x 2 - x 53. ƒ1x2 = -21x - 122 + 4, or ƒ1x2 = -2x2 + 4x + 2 55. linear; positive 57. quadratic; positive 59. quadratic; negative 61. (a) ƒ1t2 = -16t 2 + 200t + 50 (b) 6.25 sec; 675 ft (c) between 1.41 and 11.09 sec (d) 12.75 sec 63. (a) 640 - 2x (b) 0 6x 6320 (c) 1x2 = -2x 2 + 640x (d) between 57.04 ft and 85.17 ft or 234.83 ft and 262.96 ft (e) 160 ft by 320 ft; The maximum area is 51,200 ft2. 65. (a) 2x (b) length: 2x - 4; width: x - 4; x 74 (c) V1x2 = 4x2 - 24x + 32 (d) 8 in. by 20 in. (e) 13.05 in. to 14.22 in. 67. (a) 23.32 ft per sec (b) 12.88 ft 69. 10 and 10 71. 1 sec; 16 ft 73. 92.3 billion 75. 250 slices; $120 77. (a) 0 0 25 20 (b) ƒ1x2 = -0.02634x2 + 0.7289x + 15.12 (c) 0 0 25 20 The graph of ƒ models the data closely. (d) 19.7 million 79. (a) 0 0 15 100 (b) ƒ1x2 = 0.00551x - 4022 + 4.7 (c) 0 0 15 100 The graph of ƒ models the data closely. (d) g1x2 = 0.003896x2 - 0.2990x + 11.32 (e) ƒ1922 = 19.6%; g1922 = 16.8% 81. c = 25 83. ƒ1x2 = 1 2 x 2 - 7 2 x + 5 85. 13, 62 87. x y 7 –8 2 –4 0 f(x) = x2 + 2x – 8 88. -4 and 2; 5-4, 26 89. 1-4, 22 90. 1-∞, -42 ´12, ∞2 91. 1-2, 32 93. A -∞, - 3 2D ´36, ∞2 95. C 2 - 25, 2 + 25 D 3.2 Exercises 1. 3; 4 3. 1; 1 5. 3; 6; 0 7. x2 + 2x + 9 9. 5x3 + 2x - 3 11. x3 + 2x + 1 13. x4 + x3 + 2x - 1 + 3 x + 2 15. -9x2 - 10x - 27 + -52 x - 2 17. 1 3 x 2 - 1 9 x + 1 27 19. x3 - x2 - 6x 21. x2 + x + 1 23. x4 - x3 + x2 - x + 1 25. ƒ1x2 = 1x + 1212x2 - x + 22 - 10 27. ƒ1x2 = 1x + 221x2 + 2x + 12 + 0 29. ƒ1x2 = 1x - 3214x3 + 9x2 + 7x + 202 + 60 31. ƒ1x2 = 1x + 1213x3 + x2 - 11x + 112 + 4 33. 0 35. -1 37. -6 39. -6 - i 41. 0 43. -5 45. 7 47. yes 49. yes 51. no; -9 53. yes 55. no; 357 125 57. yes 59. no; 13 + 7i 61. yes
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