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454 Chapter 5 Quadratic Functions

Version: Fall 2007

In Exercises 33 -38 , nd the vertex of the graph of the given quadratic func-tion.

33. f (x) = − 2x

2

+ 5 x + 334. f (x) = x2 + 5 x + 8

35. f (x) = − 4x 2 − 4x + 1

36. f (x) = 5 x2 + 7 x + 8

37. f (x) = 4 x2 + 2 x + 8

38. f (x) = x2 + x − 7

In Exercises 39 -44 , nd the axis of sym-metry of the graph of the given quadraticfunction.

39. f (x) = − 5x 2 − 7x − 8

40. f (x) = x2 + 6 x + 3

41. f (x) = − 2x 2 − 5x − 8

42. f (x) = − x2 − 6x + 2

43. f (x) = − 5x 2 + x + 6

44. f (x) = x2 − 9x − 6

For each of the quadratic functions inExercises 45 -66 , perform each of thefollowing tasks.

i. Use the technique of completing thesquare to place the given quadraticfunction in vertex form.

ii. Set up a coordinate system on a sheetof graph paper. Label and scale eachaxis.

iii. Draw the axis of symmetry and labelit with its equation. Plot the vertexand label it with its coordinates.

iv. Set up a table near your coordinatesystem that calculates the coordinatesof two points on either side of the axisof symmetry. Plot these points and

their mirror images across the axis of symmetry. Draw the parabola andlabel it with its equation

v. Use the graph of the parabola to de-termine the domain and range of thequadratic function. Describe the do-main and range using interval nota-tion.

45. f (x) = x2 − 8x + 12

46. f (x) = x2 + 4 x − 1

47. f (x) = x2 + 6 x + 3

48. f (x) = x2 − 4x + 1

49. f (x) = x2 − 2x − 6

50. f (x) = x2 + 10 x + 23

51. f (x) = − x2 + 6 x − 4

52. f (x) = − x2 − 6x − 3

53. f (x) = − x2 − 10x − 21

54. f (x) = − x2 + 12 x − 33

55. f (x) = 2 x2 − 8x + 3

56. f (x) = 2 x2 + 8 x + 4

57. f (x) = − 2x2 − 12x − 13

58. f (x) = − 2x2 + 24 x − 70

59. f (x) = (1 / 2)x2 − 4x + 5

60. f (x) = (1 / 2)x2 + 4 x + 6

61. f (x) = ( − 1/ 2)x2 − 3x + 1 / 2

62. f (x) = ( − 1/ 2)x2 + 4 x − 2



Section 5.2 Vertex Form 455

Version: Fall 2007

63. f (x) = 2 x2 + 7 x − 2

64. f (x) = − 2x2 − 5x − 4

65. f (x) = − 3x

2

+ 8 x − 366. f (x) = 3 x2 + 4 x − 6

In Exercises 67 -72 , nd the range of the given quadratic function. Expressyour answer in both interval and set no-tation.

67. f (x) = − 2x2 + 4 x + 3

68. f (x) = x2 + 4 x + 8

69. f (x) = 5 x2 + 4 x + 4

70. f (x) = 3 x2 − 8x + 3

71. f (x) = − x2 − 2x − 7

72. f (x) = x2 + x + 9

Drill for Skill. In Exercises 73 -76 ,evaluate the function at the given value

b.73. f (x) = 9 x2 − 9x + 4 ; b = − 6

74. f (x) = − 12x 2 + 5 x + 2 ; b = − 3

75. f (x) = 4 x2 − 6x − 4; b = 11

76. f (x) = − 2x2 − 11x − 10; b = − 12

Drill for Skill. In Exercises 77 -80 ,evaluate the function at the given expres-sion.

77. Evaluate f (x +4) if f (x) = − 5x2 +4x + 2 .

78. Evaluate f (− 4x− 5) if f (x) = 4 x2 +x + 1 .

79. Evaluate f (4x − 1) if f (x) = 4 x2 +3x − 3.

80. Evaluate f (− 5x− 3) if f (x) = − 4x2 +

x + 4 .




Version: Fall 2007

5.2 Answers

1. x2

+ 85x +

1625

3. x2 + 6 x + 9

5. x2 − 14x + 49

7. x2 − 12x + 36

9. x − 35

2

11. (x − 6)2

13. (x + 6) 2

15. (x + 9) 2

17. x − 12

2

+ 31

4

19. x − 52

2

− 41

4

21. (x + 1) 2 − 7

23. x − 92

2

− 69

4

25. − 2 x + 94

2

+ 57

8

27. 5 x + 12

2

+ 15

4

29. 5 x + 7

10

2

− 109

20

31. − 1 x + 12

2

+ 17

4

33.54

, 498

35. − 12, 2

37. −14

, 314

39. x = − 710

41. x = −54

43. x = 110

45. f (x) = ( x − 4)2 − 4

x10

y10

x=4

(4,− 4)(4,− 4)

f (x)= x 2 − 8x+12

Domain = R , Range = [− 4, ∞ )




Version: Fall 2007

47. f (x) = ( x + 3) 2 − 6

x10

y10

f (x)= x 2 +6 x+3

x= − 3

(− 3,− 6)(− 3,− 6)

Domain = R , Range = [− 6, ∞ )49. f (x) = ( x − 1)2 − 7

x10

y10

f (x)= x 2 − 2x− 6

x=1

(1,− 7)(1,− 7)


51. f (x) = − (x − 3)2 + 5

x10

y10

f (x)= − x 2 +6 x− 4

x=3

(3,5)(3,5)

Domain = R , Range = ( −∞ , 5]53. f (x) = − (x + 5) 2 + 4

x10

y10

f (x)= − x2 − 10x− 21

x= − 5

(− 5,4)(− 5,4)

Domain = R , Range = ( −∞ , 4]




Version: Fall 2007

55. f (x) = 2( x − 2)2 − 5

x10

y10 f (x)=2 x 2 − 8x+3

x=2

(2,− 5)(2,− 5)


57. f (x) = − 2(x + 3) 2 + 5

x10

y10

f (x)= − 2x 2 − 12x− 13

x= − 3

(− 3,5)(− 3,5)

Domain = R , Range = ( −∞ , 5]

59. f (x) = (1 / 2)(x − 4)2 − 3

x10

y10

f (x)=(1 / 2)x 2 − 4x+5

x=4

(4,− 3)(4,− 3)

Domain = R , Range = [− 3, ∞ )61. f (x) = ( − 1/ 2)(x + 3) 2 + 5

x10

y10

f (x)=( − 1/ 2)x2 − 3x+1 / 2x= − 3

(− 3,5)(− 3,5)

Domain = R , Range = ( −∞ , 5])




Version: Fall 2007

63. f (x) = 2( x + 7 / 4)2 − 65/ 8

x10

y10 f (x)=2 x 2 +7 x− 2

x= − 7/ 4

(− 7/ 4,− 65/ 8)(− 7/ 4,− 65/ 8)

Domain = R , Range = [− 65/ 8, ∞ )

65. f (x) = − 3(x − 4/ 3)2 + 7 / 3

x10

y10

f (x)= − 3x2 +8 x− 3x=4 / 3

(4/ 3,7/ 3)(4/ 3,7/ 3)

Domain = R , Range = ( −∞ , 7/ 3]

67. (−∞ , 5] = {x |x ≤ 5}

69.165

, ∞ = x x ≥ 16

5

71. (−∞ , − 6] = {x |x ≤ − 6}

73. 382

75. 414

77. − 5x2 − 36x − 62

79. 64x2 − 20x − 2

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