456 Chapter 8Graphing Quadratic FunctionsIn Exercises 37–42, use zeros to graph the function. (See Example 5.)37. f (x) (x + 2)(x 6) 38. g(x) 3(x + 1)(x + 7)39. y x2 11x + 18 40. y x2 x 3041. y 5x2 10x + 40 42. h(x) 8x2 8ERROR ANALYSIS In Exercises 43 and 44, describe and correct the error in nding the zeros of the function.43. y=5(x 3)(x − 2)The zeros of the function are3 and −2.✗
44. y=(x 4)(x2 − 9)The zeros of the function are −4 and 9.✗
In Exercises 45–56, write a quadratic function in standard form whose graph satis es the given condition(s). (See Example 6.)45. vertex: (7, 3) 46. vertex: (4, 8)47.x-intercepts: 1 and 9 48. x-intercepts: 2 and 549. passes through (4, 0), (3, 0), and (2, 18) 50. passes through (5, 0), (1, 0), and (4, 3)51. passes through (7, 0)52. passes through (0, 0) and (6, 0)53. axis of symmetry: x 554. y increases as x increases when x< 4; y decreases as xincreases when x> 4.55. range: y ≥ 3 56. range: y ≤ 10In Exercises 57–60, write the quadratic function represented by the graph. 57. 413xy248(3, 0)(1, 8)(2, 0) 58. (1, 0)(7, 0)(6, 5)48y246x59. (2, 32)(4, 0)(2, 0)143514y1x33 60. (6, 0)(10, 0)(8, 2)224y48xIn Exercises 61–68, use zeros to graph the function. (See Example 7.)61. y 5x(x + 2)(x 6) 62. f (x) x(x + 9)(x + 3) 63. h(x) (x 2)(x + 2)(x + 7) 64. y (x + 1)(x 5)(x 4)65. f (x) 3x3 48x 66. y 2x3 + 20x2 50x67.y x3 16x2 28x68. g(x) 6x3 + 30x2 36xIn Exercises 69–72, write the cubic function represented by the graph. (See Example 8.)69. (1, 0)(4, 0)(1, 24)135xy(0, 0)4832 70. (3, 0)413xy120(1, 36)(2, 0)(0, 0)71. xy4016513(2, 40)(4, 0)(7, 0)(0, 0) 72. 32161624xy(5, 40)(3, 0)(1, 0)(6, 0)In Exercises 73–76, write a cubic function whose graph satis es the given condition(s).73. x-intercepts: 2, 3, and 874. x-intercepts: 7, 5, and 075. passes through (1, 0) and (7, 0)76. passes through (0, 6)