334 CHAPTER 3 Polynomial and Rational Functions 22. Concept Check A quadratic function ƒ1x2 has vertex 10, 02, and all of its intercepts are the same point. What is the general form of its equation? Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1– 4. 23. ƒ1x2 = 1x - 222 24. ƒ1x2 = 1x + 422 25. ƒ1x2 = 1x + 322 - 4 26. ƒ1x2 = 1x - 522 - 4 27. ƒ1x2 = - 1 2 1x + 122 - 3 28. ƒ1x2 = -31x - 222 + 1 29. ƒ1x2 = x2 - 2x + 3 30. ƒ1x2 = x2 + 6x + 5 31. ƒ1x2 = x2 - 10x + 21 32. ƒ1x2 = 2x2 - 4x + 5 33. ƒ1x2 = -2x2 - 12x - 16 34. ƒ1x2 = -3x2 + 24x - 46 35. ƒ1x2 = - 1 2 x2 - 3x - 1 2 36. ƒ1x2 = 2 3 x2 - 8 3 x + 5 3 Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. See Example 2. 37. ƒ1x2 = 1x + 322 38. ƒ1x2 = 1x - 122 39. ƒ1x2 = -1x - 222 - 5 40. ƒ1x2 = -1x + 422 + 3 41. ƒ1x2 = x2 - 4x + 3 42. ƒ1x2 = x2 - 10x + 4 43. ƒ1x2 = -2x2 - 8x - 7 44. ƒ1x2 = -3x2 + 18x + 1 Concept Check Several graphs of the quadratic function ƒ1x2 = ax2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) 45. a 60; b2 - 4ac = 0 46. a 70; b2 - 4ac 60 47. a 60; b2 - 4ac 60 48. a 60; b2 - 4ac 70 49. a 70; b2 - 4ac 70 50. a 70; b2 - 4ac = 0 A. x y 0 B. x y 0 C. x y 0 D. x y 0 E. x y 0 F. x y 0
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