Skill Building In Problems 11-24, find the zeros of each quadratic function by factoring. What are the x-intercepts of the graph of the function? 11. f(x) = x - 9x 15. F(x) = x+x-6 19. P(x) = 3x - 48 23. G(x) = 4x + 9 - 12x 12. f(x) = x + 4x 16. H(x) = x + 7x+6 13. g(x) = x - 25 17. g(x) = 2x25x - 3 20. H(x) = 2x - 50 21. g(x) = x(x+8) + 12 14. G(x) = x 9 18. f(x) = 3x + 5x + 2 22. f(x) = x(x 4) - 12 24. F(x) = 25x + 16 - 40x In Problems 25-30, find the zeros of each quadratic function using the Square Root Method. What are the x-intercepts of the graph of the function? 25. f(x) = x - 8 28. G(x) = (x + 2) - 1 26. g(x) = x - 18 29. F(x) = (2x+3) - 32 27. g(x) 30. g(x) = (x-1) - 4 (3x-2) - 75 In Problems 31-36, find the zeros of each quadratic function by completing the square. What are the x-intercepts of the graph of the function? 31. f(x) = x+4x-8 2 34. g(x) = x + - 3% 1 3 32. f(x) = x-6x - 9 35. F(x) 3x + x = - 1 2 1 3 33. g(x) = x - -x 16 36. G(x) = 2x - 3x - 1 In Problems 37-50, find the real zeros, if any, of each quadratic function using the quadratic formula. What are the x-intercepts, if any, of the graph of the function? 37. f(x) = x - 4x + 2 41. F(x) = 2x - 5x + 3 45. f(x) = 4x - 1 + 2x 49. P(x) = 9x-6x + 1 = 38. f(x) x + 4x + 2 42. g(x) = 2x + 5x + 3 46. f(x) = 2x 1 + 2x 50. g(x) = 4x + 20x + 25 39. g(x) = x - 4x - 1 43. P(x) = 4x - x + 2 47. G(x) = 2x(x + 2) 3 40. g(x) 44. H(x) 48. F(x) = = x + 6x + 1 = 4x + x + 1 3x(x + 2) - 1 In Problems 51-56, solve f(x) = g(x). What are the points of intersection of the graphs of the two functions? 51. f(x) g(x) = x + 6x + 3 = 3 54. f(x) g(x) 3x-7 = 10x + 1 52. f(x) = x - 4x + 3 g(x) = 3 55. f(x) = xx + 1 g(x) = 2x2 3x - 14 - 53. f(x) -2x + 1 g(x) = 3x + 2 56. f(x) = x + 5x g(x) 3 2x+7x27 - In Problems 57-74, find the real zeros of each function. What are the x-intercepts of the graph of the function? 57. P(x) = x-6x - 16 60. f(x) = x - 10x + 24 58. H(x) x4 -3x - 4 61. G(x) = 3x4 - 2x - 1 59. f(x) = x4 62. F(x) = 2x4 5x + 4 5x - 12 In Problems 19-28, find an equation for the hyperbola described. Graph the equation. 19. Center at (0, 0); focus at (3,0); vertex at (1,0) 21. Center at (0,0); focus at (0, -6); vertex at (0, 4) 23. Foci at (-5,0) and (5,0); vertex at (3,0) 25. Vertices at (0, -6) and (0, 6); asymptote the line y = 2x 27. Foci at (-4, 0) and (4,0); asymptote the line y = -x 20. Center at (0, 0); focus at (0,5); vertex at (0,3) 22. Center at (0, 0); focus at (-3, 0); vertex at (2,0) 24. Focus at (0,6); vertices at (0, -2) and (0,2) 26. Vertices at (-4,0) and (4,0); asymptote the line y = 2x 28. Foci at (0, -2) and (0, 2); asymptote the line y = -x 690 CHAPTER 9 Analytic Geometry In Problems 29-36, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation. x 29. - 25 9 = 1 33. y = 9x = 9 y2 30. - x 16 4 = 1 34. x - y 4 In Problems 37-40, write an equation for each hyperbola. 37. 38. y= -x y = 3 y= 3 31. 4x2 y2 = 16 - 32. 4y2x216 35. yx = 25 36. 2x2 y = 4 39. y = -2x y=2x 40. 10 y= -2x y = 2x **** 3 3 y= -x 5 5 x In Problems 41-48, find an equation for the hyperbola described. Graph the equation. 41. Center at (4, -1); focus at (7, -1); vertex at (6, 1) 43. Center at (-3, -4); focus at (-3, -8); vertex at (3, 2) 42. Center at (-3, 1); focus at (3, 6); vertex at (3,4) 44. Center at (1,4); focus at (2, 4); vertex at (0, 4)