Complete the square for each expression. Write the resulting expression as a binomial squared. 34. x 2 - 16x +. 35. x 2 + 22x +. 36. x 2 + 7x +. Solve...
Graph each function by using a table. 1 x2 - 4 1. f (x) = _ 2. f (x) = 2x 2 - x + 3 3. f (x) = -x 2 - 3x 2 Using the graph of f(x) = x 2 as a guide, describe the transformations, and then graph each function. 1 x2 4. g (x) = (x + 2)2 + 1 5. g (x) = -2x 2 6. g (x) = _ 4 Use the description to write each quadratic function in vertex form. 7. The parent function f (x) = x 2 is vertically stretched by a factor of 3 and translated 6 units right to create g. 8. The parent function f (x) = x 2 is reflected across the x-axis and translated 12 units down to create g.
Lesson
2-2
Identify the axis of symmetry for the graph of each function. 9. f (x) = 2x 2 + 1 10. f (x) = (x + 3)2 - 5 11. f (x) = 3(x - 2)2 For each function, (a) determine whether the graph opens upward or downward, (b) find the axis of symmetry, (c) find the vertex, (d) find the y-intercept, and (e) graph the function. 1 x 2 - 2x + 3 12. f (x) = 2x 2 - 4x + 5 13. f (x) = -_ 14. f (x) = -x 2 - 8x - 6 2 Find the minimum or maximum value of each function. Then state the domain and range of the function. 15. f (x) = 3x 2 + 60x + 294 16. f (x) = -2x 2 + 28x - 95 17. f (x) = 2x 2 + 14x + 30
Lesson
2-3
Find the zeros of each function by using a graph and a table. 18. f (x) = x 2 + 5x + 6 19. f (x) = x 2 - 3x - 28 20. f (x) = -x 2 + 12x - 20 Find the zeros of each function by factoring. 21. f (x) = x 2 + 2x - 35 22. f (x) = x 2 - 8x - 9
23. f (x) = 2x 2 - 9x
24. f (x) = x 2 + 10x + 25
26. f (x) = x 2 - 12x + 36
25. f (x) = x 2 - 49
Write a quadratic function in standard form for each given set of zeros. 27. 5 and 8 28. -3 and 1 29. 6 and 6 30. 12 and 0 Lesson
2-4
Solve each equation. 31. 4x 2 - 10 = 90
32. x 2 + 8x + 16 = 10
33. x 2 + 4x + 4 = 8
Complete the square for each expression. Write the resulting expression as a binomial squared. 34. x 2 - 16x + 35. x 2 + 22x + 36. x 2 + 7x + Solve each equation by completing the square. 37. x 2 + 8x = -10 38. x 2 - 12x = 13
39. x 2 + 20 = 10x
40. 2x 2 + 12x = 14
42. x 2 - 5 = 2x
41. 3x 2 - 18 = 48x
Write each function in vertex form, and identify its vertex. 43. f (x) = x 2 - 2x + 17 44. f (x) = x 2 + 4x - 8 45. f (x) = 4x 2 - 24x + 31
EPS4
Extra Practice Chapter 2 Lesson
2-5
Skills Practice
Express each number in terms of i. 46. 2 √ -81 47. - √ -144 Solve each equation. 50. 169 + x 2 = 0
48. √ -128
51. 2x 2 = -200
52. x 2 = -90
Find the zeros of each function. 53. f (x) = x 2 + 8x + 20 54. f (x) = x 2 - 14x + 65 Find each complex conjugate. 56. 12i 57. 3 - 6i Lesson
2-6
49. 5 √ -48
55. f (x) = x 2 - 2x + 46 59. 2 √ 7 - 10i
58. 10i - 3
Find the zeros of each function by using the Quadratic Formula. 60. f (x) = x 2 - 10x + 3 61. f (x) = 2x 2 + 5x + 1 62. f (x) = -x 2 + 8x - 3 63. f (x) = x 2 - 6x + 40
64. f (x) = x 2 + 7x + 13
65. f (x) = 2x 2 - 9x + 25
Find the type and number of solutions for each equation. 67. x 2 + 3 = 10x 68. 5 + 2x 2 = 12x 66. x 2 + 8x = -16 Lesson
2-7
Lesson
2-8
69. 4x 2 + 2x = -9
Graph each inequality. 70. y ≥ (x + 3)2 + 2
71. y < 2x 2 - 4x - 1
72. y < -x 2 + 11x - 24
Solve each inequality. 73. x 2 + 13x + 20 < -2
74. x 2 - 11x ≥ -10
75. x 2 + 6x + 3 > 10
76. x 2 - 2x - 20 > 28
77. 2x 2 - 9x ≤ 5
78. 3x 2 + 1 ≥ 4x
Determine whether each data set could represent a quadratic function. Explain. 79. x 3 4 5 6 7 80. x -2 -1 0 1 2 81. x -6 -5 -4 -3 -2 y
-2 -5 -6 -5 -2
y
-5
2
3
4
11
y
19 10
7
10 19
Write a quadratic function that fits each set of points. 82. (-2, 0), (1, 6), and (3, -10) 83. (-4, -25), (0, -9), and (2, 5) Lesson
2-9
Graph each complex number. 84. -3 85. 2i Find each absolute value. 88. ⎪6 + 9i⎥
86. 2 + 4i
89. ⎪-3 + 4i⎥
Simplify. Write the result in the form a + bi. 91. (3 + 7i) + (-2 + 3i) 92. (-9 - 4i) + (5 + i)
