Section 8.4 Graphing f (x) a(x h)2 + k 447In Exercises 31–34, nd the vertex and the axis of symmetry of the graph of the function.31. y 6(x + 4)2 3 32. f (x) 3(x 3)2 + 633. f (x) 4(x + 3)2 + 1 34. y (x 6)2 5In Exercises 35–38, match the function with its graph. 35. y (x + 1)2 3 36. y 1 — 2 (x 1)2 + 337. y 1 — 3 (x 1)2 + 3 38. y 2(x + 1)2 3 A. 1133x13y B. 21x24y C. 246x242y D. 26x224yIn Exercises 39–44, graph the function. Compare the graph to the graph of f (x) = x2. (See Example 3.) 39. h(x) (x 2)2 + 4 40. g(x) (x + 1)2 741. r(x) 4(x 1)2 5 42. n(x) (x + 4)2 + 243. g(x) 1 — 3 (x + 3)2 2 44. r(x) 1 — 2 (x 2)2 4In Exercises 45–48, let f (x) = (x − 2)2 1. Match the function with its graph.45. g(x) f (x 1) 46. r(x) f (x + 2)47.h(x) f (x) + 2 48. p(x) f (x) 3 A. 24x246y B. 246x24y C. 246x22y D. 22x24yIn Exercises 49–54, graph g. (See Example 4.)49. f (x) 2(x 1)2 + 1; g(x) f (x + 3)50. f (x) (x + 1)2 + 2; g(x) 1 — 2 f (x)51. f (x) 3(x + 5)2 6; g(x) 2f (x)52. f (x) 5(x 3)2 1; g(x) f (x) 653. f (x) (x + 3)2 + 5; g(x) f (x 4)54. f (x) 2(x 4)2 8; g(x) f (x)55. MODELING WITH MATHEMATICS The height (inmeters) of a bird diving to catch a sh is represented by h(t) 5(t 2.5)2, where t is the number of seconds after beginning the dive. a. Graph h. b. Another bird’s dive is represented by r(t) 2h(t). Graph r. c. Compare the graphs. Which bird starts its dive from a greaterheight? Explain. 56. MODELING WITH MATHEMATICS A kicker punts a football. The height (in yards) of the football is represented by f (x) 1 — 9 (x 30)2 + 25, where x isthe horizontal distance (in yards) from the kicker’s goal line. a. Graph f. Describe the domain and range. b. On the next possession, the kicker punts the football. The height of the football is represented by g(x) f (x + 5). Graph g. Describe the domain and range. c. Compare the graphs. On which possession does the kicker punt closer to his goal line? Explain.In Exercises 57–62, write a quadratic function in vertex form whose graph has the given vertex and passes through the given point. 57. vertex: (1, 2); passes through (3, 10) 58. vertex: (3, 5); passes through (0, 14) 59. vertex: (2, 4); passes through (1, 6) 60. vertex: (1, 8); passes through (3, 12) 61. vertex: (5, 2); passes through (7, 0) 62. vertex: (5, 1); passes through (2, 2)