Chap5 Section2

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 5.2 Vertex Form 453 Version: Fall 2007 5.2 Exercises In Exercises 1 - 8 , expand the binomial. 1. x + 4 5 2 2. x 4 5 2 3. ( x + 3) 2 4. ( x + 5) 2 5. ( x 7) 2 6. x 2 5 2 7. ( x 6) 2 8. x 5 2 2 In Exercises 9 - 16 , factor the perfect square trinomial. 9. x 2 6 5 x + 9 25 10. x 2 + 5 x + 25 4 11. x 2 12 x + 36 12. x 2 + 3 x + 9 4 13. x 2 + 12 x + 36 14. x 2 3 2 x + 9 16 15. x 2 + 18 x + 81 Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 16. x 2 + 10 x + 25 In Exercises 17 - 24 , transform the given quadratic function into vertex form f ( x ) = ( x h ) 2 + k by completing the square. 17. f ( x ) = x 2 x + 8 18. f ( x ) = x 2 + x 7 19. f ( x ) = x 2 5 x 4 20. f ( x ) = x 2 + 7 x 1 21. f ( x ) = x 2 + 2 x 6 22. f ( x ) = x 2 + 4 x + 8 23. f ( x ) = x 2 9 x + 3 24. f ( x ) = x 2 7 x + 8 In Exercises 25 - 32 , transform the given quadratic function into vertex form f ( x ) = a ( x h ) 2 + k by completing the square. 25. f ( x ) = 2 x 2 9 x 3 26. f ( x ) = 4 x 2 6 x + 1 27. f ( x ) = 5 x 2 + 5 x + 5 28. f ( x ) = 3 x 2 4 x 6 29. f ( x ) = 5 x 2 + 7 x 3 30. f ( x ) = 5 x 2 + 6 x + 4 31. f ( x ) = x 2 x + 4 32. f ( x ) = 3 x 2 6 x + 4
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454 Chapter 5 Quadratic Functions Version: Fall 2007 In Exercises 33 - 38 , find the vertex of the graph of the given quadratic func- tion. 33. f ( x ) = 2 x 2 + 5 x + 3 34. f ( x ) = x 2 + 5 x + 8 35. f ( x ) = 4 x 2 4 x + 1 36. f ( x ) = 5 x 2 + 7 x + 8 37. f ( x ) = 4 x 2 + 2 x + 8 38. f ( x ) = x 2 + x 7 In Exercises 39 - 44 , find the axis of sym- metry of the graph of the given quadratic function. 39. f ( x ) = 5 x 2 7 x 8 40. f ( x ) = x 2 + 6 x + 3 41. f ( x ) = 2 x 2 5 x 8 42. f ( x ) = x 2 6 x + 2 43. f ( x ) = 5 x 2 + x + 6 44. f ( x ) = x 2 9 x 6 For each of the quadratic functions in Exercises 45 - 66 , perform each of the following tasks. i. Use the technique of completing the square to place the given quadratic function in vertex form. ii. Set up a coordinate system on a sheet of graph paper. Label and scale each axis. iii. Draw the axis of symmetry and label it with its equation. Plot the vertex and label it with its coordinates. iv. Set up a table near your coordinate system that calculates the coordinates of two points on either side of the axis of symmetry. Plot these points and their mirror images across the axis of symmetry. Draw the parabola and label it with its equation v. Use the graph of the parabola to de- termine the domain and range of the quadratic function. Describe the do- main and range using interval nota- tion. 45. f ( x ) = x 2 8 x + 12 46. f ( x ) = x 2 + 4 x 1 47. f ( x ) = x 2 + 6 x + 3 48. f ( x ) = x 2 4 x + 1 49. f ( x ) = x 2 2 x 6 50. f ( x ) = x 2 + 10 x + 23 51. f ( x ) = x 2 + 6 x 4 52. f ( x ) = x 2 6 x 3 53. f ( x ) = x 2 10 x 21 54. f ( x ) = x 2 + 12 x 33 55. f ( x ) = 2 x 2 8 x + 3 56. f ( x ) = 2 x 2 + 8 x + 4 57. f ( x ) = 2 x 2 12 x 13 58. f ( x ) = 2 x 2 + 24 x 70 59. f ( x ) = (1 / 2) x 2 4 x + 5 60. f ( x ) = (1 / 2) x 2 + 4 x + 6 61. f ( x ) = ( 1 / 2) x 2 3 x + 1 / 2 62. f ( x ) = ( 1 / 2) x 2 + 4 x 2
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Section 5.2 Vertex Form 455 Version: Fall 2007 63. f ( x ) = 2 x 2 + 7 x 2 64. f ( x ) = 2 x 2 5 x 4 65. f ( x ) = 3 x 2 + 8 x 3 66. f ( x ) = 3 x 2 + 4 x 6 In Exercises 67 - 72 , find the range of the given quadratic function. Express your answer in both interval and set no- tation.
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