DOC100217-10022017141901.pdf

DOC100217-10022017141901.pdf - 5 f(x)= 3x2 5x 2_f(x)=(x...

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Unformatted text preview: 5. f(x)= 3x2+5x* 2 -_f(x)=(x+1)2—2 f(x)= (x—4)2 +2 ’f(x)= -(x+1)2—3 _f(X) = —3(x + 2)2 — 15 “Ti-E-f(x)=x2+6x— 3 Lflx): sz — 12x + 6 111*): ‘4x2 + 16x w 7 f(x) = —4x2 + 12x — 2 " In Exercises 5—8, match the quadratic function with its graph. _ f(x) = —0.5(x e 0.25)2 + 0.75 6.f(x)=3x2*xw2 7.f(x)=—x2+2x*l 10. fix) 2 (x- + 2)2 — 1 13. fix) = —(x — 3.)2 + 9 16. fix) = ~(x # 2)2 + 6' 19- f{x) = (x e if +% 22. fix) : "-0.20: + 0.6)2 + 0.8 24. f(x) = x2 + 8x + 2 27. fix) = 2x2 + 8x ~ 2 30. f(x) = 7512 + 100x — 36 33. fix) : %x2 — 4x + 3 2.1 Quadratic Functions 207 8. f(x) = —2x2 — x + 3 11. fix) = (x — 2)2 — 3 14. fix) = —(x — 5)2 ~ 4 17. fix) = 2(x e 2)2 + 2 20. fix) = (x +1)2 7% EXercises 23—34, rewrite the quadratic function in standard form by completing the square. 25. fix) = —x2 — 10x + 3 28. f(x) = 3x2 - 9x +11 31. f(x) = x2 + 10x 34. fix) : “%x2 + 6x + 4 f5 11' 1 Ii '1 208 CHAPTER 2 Polynomial and Rationai Function-.5 In Exercises 35—44, graph the quadratic function. 35. f(x) = x2 + 6x " 7' 39. fix) = 4x2 — 5x + 10 43. f(x) = %x2 — % 36. f(x) 2 x2 — 3x + 10 40. f(x) = 3x2 + 9x — 1 44. f(x) : ~§8 +§ 37. f(x) 2 ~23“ f it + 6 41. f(x) : —2x2 - 12x — 16 In Exercises 45—54, find the vertex of the parabola associated with each quadratic function. 45. fix) = 33x2 — 2x + 15 47. f(x) 2 if 7 7x + 5 49. f(x) = —§x2 + %x + 2- 51. f(x) = —0.002x2 - 0.3x + 1.7 53. f(x) = 0.06):2 — 2.6x + 3.52 46. f(x) = 17x2 + 4x 7 3 4s. f(x) : —§x2 + §x + 4 50. fix) = ea? , gx + g 52. fix) : 0.05;:2 + 2.5x v 1.5 54. f(x) = 4.2).? + 0.8x — 0.14 38. fix) 2 7x1 + 3x + 4 42. f(x) = —3x2 +121" — 12 In Exercises 55—66, find the quadratic function that has the given vertex and goes through the given point. 55. vertex: (—1.4) 58. vertex: (1, 3) 61. vertex: (-2, —4} point: (0, 2) point: (—2, 0) 56. vertex: (2, e3) 59. vertex: (—1. —3) point: (— 1, 6) 62. vertex: (5, 4) point: (0, 0) 65. vertex: (2.5, ~35) 57. vertex: (2, 5) 60. vertex: (0, —2) 63. vertex: (i —%) 66. vertex: (1.8, 2.7) point: (3, 0) point: (3, 10) point: (i 0) point: (—2.2, —2.ll) point: (0, 1) point: (—4, 2) point: (2:5) point: (4.5, 1.5) Exercises 67 and 68 concern the path of a punted football. Refer to the diagram in Example 9. 67. Sports. The path of a particular punt follows the quadratic function _ 8 2 11(x) 125 (x + 5) ~t- 40 where h(x) is the height of the bail in yards and x corresponds to the horizontal distance in yards. Assume x = 0 conesponds to midfield (the 50 yard line). For example, 2: = #20 corresponds to the punter’s own 30 yard line, whereas I = 20 corresponds to the other team’s 30 yard line. 3. Find the maximum height the ball achieves. b. Find the horizontal distance the ball covers. Assume the height is zero when the ball is kicked and when the ball is caught. 68. Sports. The path of a particular punt follows the quadratic function 5 2 z ,7 , , + h(x) 40(21 30) 50 where h(x) is the height of the ball in yards and x corresponds to the horizontal distance in yards. Assume .1; = 0 corresponds to midfield (the 50 yard line). For example. x 2 720 corresponds to the punter’s own 30 yard line, whereas .r = 20 corresponds to the other team's 30 yard line. a. Find the maximum height the ball achieves. b. Find the horizontal distance the ball covers. Assume the height is zero when the ball is kicked and when the ball is caught. 69. Ranching. A rancher has 10,000 linear feet of fencing and wants to enclose a rectangular field and then divide it into two equal pastures with an internal fence parallel to one of the rectangular sides. What is the maximum area of each pasture? Round to the nearest square foot. .5 70. Ranching. A rancher has 30,000 linear feet of fencing and wants to enclose a rectangular field and then divide it into four equal pastures with three internal fences parallel to one of the rectangular sides. What is the maximum area of each pasture? ...
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