1. CHAPTER 2 RevIEw
precalculus

3. y = (x+2)2

5. y = (x-2)2 -1

7. y = -(x+1)2 + 3

8. 4) The number of horsepower H required to overcome wind drag on a certain car is approximated by H(s) = 0.002s s , 0 < s < 100 where s is the speed of the car in miles per hour.
a) Use a graphing calculator to graph.
b) Estimate the maximum speed of the car if the power required to overcome wind drag is not to exceed 10 horsepower. Round your answer to the nearest tenth.

9. 4) The number of horsepower H required to overcome wind drag on a certain car is approximated by H(s) = 0.002s s , 0 < s < 100 where s is the speed of the car in miles per hour.
a) Use a graphing calculator to graph.
b) Estimate the maximum speed of the car if the power required to overcome wind drag is not to exceed 10 horsepower. Round your answer to the nearest tenth.

10. 4) The number of horsepower H required to overcome wind drag on a certain car is approximated by H(s) = 0.002s s , 0 < s < 100 where s is the speed of the car in miles per hour.
a) Use a graphing calculator to graph.
b) Estimate the maximum speed of the car if the power required to overcome wind drag is not to exceed 10 horsepower. Round your answer to the nearest tenth.

11. 4) The number of horsepower H required to overcome wind drag on a certain car is approximated by H(s) = 0.002s s , 0 < s < 100 where s is the speed of the car in miles per hour.
a) Use a graphing calculator to graph.
b) Estimate the maximum speed of the car if the power required to overcome wind drag is not to exceed 10 horsepower. Round your answer to the nearest tenth.
59.4 MPH

12. 5) f(x) = x2 - 16

13. 5) f(x) = x2 - 16
= (x )(x )

14. 5) f(x) = x2 - 16
= (x - 4)(x + 4)

15. 5) f(x) = x2 - 16
= (x - 4)(x + 4)
zeros: 4, -4

16. 6) f(x) = x2 + 12x + 36

17. 6) f(x) = x2 + 12x + 36
= (x )(x )

18. 6) f(x) = x2 + 12x + 36
= (x + 6)(x + 6)

19. 6) f(x) = x2 + 12x + 36
= (x + 6)(x + 6)
zeros: -6, -6

20. 7) f(x) = 2x2 - 14x + 24

21. 7) f(x) = 2x2 - 14x + 24
= 2( )

22. 7) f(x) = 2x2 - 14x + 24
= 2(x2 - 7x + 12)

23. 7) f(x) = 2x2 - 14x + 24
= 2(x2 - 7x + 12)
= 2(x )(x )

24. 7) f(x) = 2x2 - 14x + 24
= 2(x2 - 7x + 12)
= 2(x - 4)(x - 3)

25. 7) f(x) = 2x2 - 14x + 24
= 2(x2 - 7x + 12)
= 2(x - 4)(x - 3)
zeros: 4, 3

26. 8) f(x) = x4 - x3 - 20x2

27. 8) f(x) = x4 - x3 - 20x2
= x2( )

28. 8) f(x) = x4 - x3 - 20x2
= x2(x2 - x - 20x)

29. 8) f(x) = x4 - x3 - 20x2
= x2(x2 - x - 20x)
= x2(x )(x )

30. 8) f(x) = x4 - x3 - 20x2
= x2(x2 - x - 20x)
= x2(x + 4)(x - 5)

31. 8) f(x) = x4 - x3 - 20x2
= x2(x2 - x - 20x)
= x2(x + 4)(x - 5)
= (x)(x)(x + 4)(x - 5)

32. 8) f(x) = x4 - x3 - 20x2
= x2(x2 - x - 20x)
= x2(x + 4)(x - 5)
= (x)(x)(x + 4)(x - 5)
zeros: 0, 0, -4, 5

33. Find a polynomial with the following zeros.
9) -7, 2

34. Find a polynomial with the following zeros.
9) -7, 2
(x - -7)(x - 2)

35. Find a polynomial with the following zeros.
9) -7, 2
(x - -7)(x - 2)
(x + 7)(x - 2)

36. Find a polynomial with the following zeros.
9) -7, 2
(x - -7)(x - 2)
(x + 7)(x - 2)
x2 - 2x + 7x - 14

37. Find a polynomial with the following zeros.
9) -7, 2
(x - -7)(x - 2)
(x + 7)(x - 2)
x2 - 2x + 7x - 14
x2 + 5x - 14

38. 10) 0, 4

39. 10) 0, 4
(x - 0)(x - 4)

40. 10) 0, 4
(x - 0)(x - 4)
x(x - 4)

41. 10) 0, 4
(x - 0)(x - 4)
x(x - 4)
x2 - 4x

42. What does the graph of each function look like? (circle two for each)
11) f(x) = -x2 + 6x + 9 rises to the left rises to the right
falls to the left falls to the right

43. What does the graph of each function look like? (circle two for each)
11) f(x) = -x2 + 6x + 9 rises to the left rises to the right
falls to the left falls to the right

44. What does the graph of each function look like? (circle two for each)
11) f(x) = -x2 + 6x + 9 rises to the left rises to the right
falls to the left falls to the right

45. 12) f(x) = 0.5x3 + 2x rises to the left rises to the right
falls to the left falls to the right

46. 12) f(x) = 0.5x3 + 2x rises to the left rises to the right
falls to the left falls to the right

47. 12) f(x) = 0.5x3 + 2x rises to the left rises to the right
falls to the left falls to the right

48. 13) f(x) = 6(x4 + 3x2 + 2) rises to the left rises to the right
falls to the left falls to the right

49. 13) f(x) = 6(x4 + 3x2 + 2) rises to the left rises to the right
falls to the left falls to the right

50. 13) f(x) = 6(x4 + 3x2 + 2) rises to the left rises to the right
falls to the left falls to the right

51. 14) f(x) = -x5 - 7x + 10 rises to the left rises to the right
falls to the left falls to the right

52. 14) f(x) = -x5 - 7x + 10 rises to the left rises to the right
falls to the left falls to the right

53. 14) f(x) = -x5 - 7x + 10 rises to the left rises to the right
falls to the left falls to the right

54. Use long division to simplify.
15) (2x3 - 3x2 - 50x + 75) / (2x - 3)

55. Use long division to simplify.
15) (2x3 - 3x2 - 50x + 75) / (2x - 3)
2x x3 - 3x2 - 50x + 75

56. Use long division to simplify.
15) (2x3 - 3x2 - 50x + 75) / (2x - 3) x2
2x x3 - 3x2 - 50x + 75

57. Use long division to simplify.
15) (2x3 - 3x2 - 50x + 75) / (2x - 3) x2
2x x3 - 3x2 - 50x + 75
2x3 - 3x2

58. Use long division to simplify.
15) (2x3 - 3x2 - 50x + 75) / (2x - 3) x2
2x x3 - 3x2 - 50x + 75
2x3 - 3x2

59. Use long division to simplify.
15) (2x3 - 3x2 - 50x + 75) / (2x - 3) x2
2x x3 - 3x2 - 50x + 75
2x3 - 3x2
x + 75

60. Use long division to simplify.
15) (2x3 - 3x2 - 50x + 75) / (2x - 3) x
2x x3 - 3x2 - 50x + 75
2x3 - 3x2
x + 75

61. Use long division to simplify.
15) (2x3 - 3x2 - 50x + 75) / (2x - 3) x
2x x3 - 3x2 - 50x + 75
2x3 - 3x2
x + 75
- 50x + 75

62. Use long division to simplify.
15) (2x3 - 3x2 - 50x + 75) / (2x - 3) x
2x x3 - 3x2 - 50x + 75
2x3 - 3x2
x + 75
- 50x + 75

63. Use long division to simplify.
15) (2x3 - 3x2 - 50x + 75) / (2x - 3) x
2x x3 - 3x2 - 50x + 75
2x3 - 3x2
x + 75
- 50x + 75

64. Use synthetic division to simplify.
16) (3x3 - 17x2 + 15x - 25) / (x - 5)

65. Use synthetic division to simplify.
16) (3x3 - 17x2 + 15x - 25) / (x - 5)

66. Use synthetic division to simplify.
16) (3x3 - 17x2 + 15x - 25) / (x - 5)

67. Use synthetic division to simplify.
16) (3x3 - 17x2 + 15x - 25) / (x - 5) 3

68. Use synthetic division to simplify.
16) (3x3 - 17x2 + 15x - 25) / (x - 5) 15 3

69. Use synthetic division to simplify.
16) (3x3 - 17x2 + 15x - 25) / (x - 5) 15

70. Use synthetic division to simplify.
16) (3x3 - 17x2 + 15x - 25) / (x - 5)

71. Use synthetic division to simplify.
16) (3x3 - 17x2 + 15x - 25) / (x - 5)

72. Use synthetic division to simplify.
16) (3x3 - 17x2 + 15x - 25) / (x - 5)

73. Use synthetic division to simplify.
16) (3x3 - 17x2 + 15x - 25) / (x - 5)

74. Use synthetic division to simplify.
16) (3x3 - 17x2 + 15x - 25) / (x - 5)
3x2 - 2x + 5

75. 17) (2x3 + 14x2 - 20x + 7) / (x + 6)

76. 17) (2x3 + 14x2 - 20x + 7) / (x + 6)

77. 17) (2x3 + 14x2 - 20x + 7) / (x + 6)

78. 17) (2x3 + 14x2 - 20x + 7) / (x + 6)

79. 17) (2x3 + 14x2 - 20x + 7) / (x + 6)
2x2 + 2x
x+6

80. Write in completely factored form. Then find all zeros.
18) f(x) = x3 + 4x2 - 25x Hint: (x - 4) is a factor

81. Write in completely factored form. Then find all zeros.
18) f(x) = x3 + 4x2 - 25x Hint: (x - 4) is a factor

82. Write in completely factored form. Then find all zeros.
18) f(x) = x3 + 4x2 - 25x Hint: (x - 4) is a factor

83. Write in completely factored form. Then find all zeros.
18) f(x) = x3 + 4x2 - 25x Hint: (x - 4) is a factor

84. Write in completely factored form. Then find all zeros.
18) f(x) = x3 + 4x2 - 25x Hint: (x - 4) is a factor
x2 + 8x + 7

85. Write in completely factored form. Then find all zeros.
18) f(x) = x3 + 4x2 - 25x Hint: (x - 4) is a factor
x2 + 8x + 7
(x + 1)(x + 7)

86. Write in completely factored form. Then find all zeros.
18) f(x) = x3 + 4x2 - 25x Hint: (x - 4) is a factor
x2 + 8x + 7
(x + 1)(x + 7)
(x - 4)(x + 1)(x + 7)

87. Write in completely factored form. Then find all zeros.
18) f(x) = x3 + 4x2 - 25x Hint: (x - 4) is a factor
x2 + 8x + 7
(x + 1)(x + 7)
(x - 4)(x + 1)(x + 7)
zeros: 4, ,

88. 19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors

89. 19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors

90. 19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors

91. 19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
x3 - x2 - 10x - 8

92. 19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
x3 - x2 - 10x - 8

93. 19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
x3 - x2 - 10x - 8

94. 19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
x3 - x2 - 10x - 8

95. 19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
x3 - x2 - 10x - 8
x2 - 3x - 4

96. 19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
x3 - x2 - 10x - 8
x2 - 3x - 4
(x - 4)(x + 1)

97. 19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
x3 - x2 - 10x - 8
x2 - 3x - 4
(x - 4)(x + 1)
(x - 4)(x + 1)(x + 2)(x - 3)

98. 19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
x3 - x2 - 10x - 8
x2 - 3x - 4
(x - 4)(x + 1)
(x - 4)(x + 1)(x + 2)(x - 3)
zeros: 4, , ,

99. Write each complex number in standard form.
20) (3 + 2i) + (5 + i)

100. Write each complex number in standard form.
20) (3 + 2i) + (5 + i)
8 + 3i

101. 21) (3 + 2i)(5 + i)

102. 21) (3 + 2i)(5 + i)
15 + 3i + 10i + 2i2

103. 21) (3 + 2i)(5 + i)
15 + 3i + 10i + 2i2
i + 2i2

104. 21) (3 + 2i)(5 + i)
15 + 3i + 10i + 2i2
i + 2i2
i + 2(-1)

105. 21) (3 + 2i)(5 + i)
15 + 3i + 10i + 2i2
i + 2i2
i + 2(-1) i

106. 22) (3 + 2i)
(5 + i)

107. 22) (3 + 2i) * (5 - i)
(5 + i) * (5 - i)

108. 22) (3 + 2i) * (5 - i) = i + 10i - 2i2
(5 + i) * (5 - i) = i - 5i - i2

109. 22) (3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2 = 15 + 7i -2(-1)

110. 22) (3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2 = 15 + 7i -2(-1)

111. 22) (3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2 = 15 + 7i -2(-1) =26

112. 22) (3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2 = 15 + 7i -2(-1) =26 i

113. Find all zeros. Then rewrite the function in completely factored form.
23) f(x) = x2 - 10x + 6

114. Find all zeros. Then rewrite the function in completely factored form.
23) f(x) = x2 - 10x + 6
A = 1
B = -10
C = 6

115. Find all zeros. Then rewrite the function in completely factored form.
23) f(x) = x2 - 10x + 6
A = 1
B = -10
C = 6

116. Find all zeros. Then rewrite the function in completely factored form.
23) f(x) = x2 - 10x + 6
A = 1
B = -10
C = 6

117. Find all zeros. Then rewrite the function in completely factored form.
23) f(x) = x2 - 10x + 6
A = 1
B = -10
C = 6

118. Find all zeros. Then rewrite the function in completely factored form.
23) f(x) = x2 - 10x + 6
A = 1
B = -10
C = 6

119. Find all zeros. Then rewrite the function in completely factored form.
23) f(x) = x2 - 10x + 6
A = 1
B = -10
C = 6 =

120. Find all zeros. Then rewrite the function in completely factored form.
23) f(x) = x2 - 10x + 6
A = 1
B = -10
C = 6 =

121. 24) f(x) = x2 + 2x + 4

122. 24) f(x) = x2 + 2x + 4
Quadratic Formula

123. 24) f(x) = x2 + 2x + 4
Quadratic Formula > Magic Happens

124. 24) f(x) = x2 + 2x + 4
Quadratic Formula > Magic Happens >

125. 24) f(x) = x2 + 2x + 4
Quadratic Formula > Magic Happens >

126. 25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4

127. 25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4

128. 25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3x3 - 7x2 + 14x - 4

129. 25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3x3 - 7x2 + 14x - 4

130. 25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3x3 - 7x2 + 14x - 4
3x3 - 7x2 + 14x - 4

131. 25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3x3 - 7x2 + 14x - 4 /
3x3 - 7x2 + 14x x2 - 6x + 12

132. 25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3x3 - 7x2 + 14x - 4 /
3x3 - 7x2 + 14x x2 - 6x + 12
Quadratic Formula

133. 25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3x3 - 7x2 + 14x - 4 /
3x3 - 7x2 + 14x x2 - 6x + 12
Quadratic Formula > Magic Happens

134. Quadratic Formula -------> Magic Happens ------->
25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3x3 - 7x2 + 14x - 4 /
3x3 - 7x2 + 14x x2 - 6x + 12
Quadratic Formula > Magic Happens >
x =
x =

135. Quadratic Formula -------> Magic Happens ------->
25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
3x3 - 7x2 + 14x - 4 /
3x3 - 7x2 + 14x x2 - 6x + 12
Quadratic Formula > Magic Happens >
x =
x =

136. 26) f(x) = x3 - 4x2 + 6x - 4

137. 26) f(x) = x3 - 4x2 + 6x - 4

138. 26) f(x) = x3 - 4x2 + 6x - 4
2, ____, ____

139. 26) f(x) = x3 - 4x2 + 6x - 4
2, ____, ____
Synthetic Division

140. 26) f(x) = x3 - 4x2 + 6x - 4
2, ____, ____
Synthetic Division > x2 - 2x + 2

141. 26) f(x) = x3 - 4x2 + 6x - 4
2, ____, ____
Synthetic Division > x2 - 2x > Quadratic Formula

142. 26) f(x) = x3 - 4x2 + 6x - 4
2, 1 + i, 1 - i
Synthetic Division > x2 - 2x > Quadratic Formula

143. 26) f(x) = x3 - 4x2 + 6x - 4
2, 1 + i, 1 - i
(x - 2)(x i)(x i)
Synthetic Division > x2 - 2x > Quadratic Formula

144. Find a polynomial with the following zeros.
27) 2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x i)(x i)
x2 - 2x + 3ix

145. Find a polynomial with the following zeros.
27) 2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x i)(x i)
x2 - 2x + 3ix - 2x i

146. Find a polynomial with the following zeros.
27) 2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x i)(x i)
x2 - 2x + 3ix - 2x i - 3ix + 6i - 9i2

147. Find a polynomial with the following zeros.
27) 2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x i)(x i)
x2 - 2x + 3ix - 2x i - 3ix + 6i - 9i2
x2 - 2x + 3ix - 2x i - 3ix + 6i - 9(-1)

148. Find a polynomial with the following zeros.
27) 2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x i)(x i)
x2 - 2x + 3ix - 2x i - 3ix + 6i - 9i2
x2 - 2x + 3ix - 2x i - 3ix + 6i - 9(-1)
x2 - 4x

149. Find a polynomial with the following zeros.
27) 2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x i)(x i)
x2 - 2x + 3ix - 2x i - 3ix + 6i - 9i2
x2 - 2x + 3ix - 2x i - 3ix + 6i - 9(-1)
x2 - 4x
x2 - 4x + 13

150. 28) 0, 3, 5i, -5i

151. 28) 0, 3, 5i, -5i
(x) (x-3) (x-5i) (x+5i)

152. 28) 0, 3, 5i, -5i
(x) (x-3) (x-5i) (x+5i)
( x2 - 3x ) (x2 + 5ix - 5ix - 25i2 )

153. 28) 0, 3, 5i, -5i
(x) (x-3) (x-5i) (x+5i)
( x2 - 3x ) (x2 + 5ix - 5ix - 25i2 )
( x2 - 3x ) (x2 + 25)

154. 28) 0, 3, 5i, -5i
(x) (x-3) (x-5i) (x+5i)
( x2 - 3x ) (x2 + 5ix - 5ix - 25i2 )
( x2 - 3x ) (x2 + 25)
x4 + 25x2 - 3x3 - 75x

155. 28) 0, 3, 5i, -5i
(x) (x-3) (x-5i) (x+5i)
( x2 - 3x ) (x2 + 5ix - 5ix - 25i2 )
( x2 - 3x ) (x2 + 25)
x4 + 25x2 - 3x3 - 75x
x4 - 3x3 + 25x2 - 75x

156. Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
29)

157. Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
29)
HA: y = -1
VA: x = -3
Holes: none

158. Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
30)

159. Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
30)
HA: y = 4
VA: x = 8
Holes: none

160. Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
31)

161. Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
31)
HA: y = 0
VA: x = -3, x = 6
Holes: none

162. Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
32)

163. Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
32)
HA: y = 0
VA: x = -1, x = 1
Holes: none

164. Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
33)

165. Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
33)
HA: y = 3
VA: none
Holes: none

166. Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
34)
hint: this one has a hole

167. Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
34)
hint: this one has a hole
HA: y = 1
VA: x = -1
Holes: x = 1
(x - 4)(x - 1)
(x + 1)(x - 1)

168. Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
35)
hint: this one has a hole

169. Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
35)
hint: this one has a hole
HA: y = 1
VA: x = -1.5
Holes: x = 3
(2x - 1)(x - 3)
(2x + 3)(x - 3)

170. 36). This table shows the amounts A (in dollars) spent per
36) This table shows the amounts A (in dollars) spent per person on the internet in the United States from 2000 to Use a graphing calculator to create a scatter plot of the data. Let t represent the year, with t = 0 corresponding to 2000.
a) Calculate a quadratic regression line to fit the data. What is its equation?
b) Based on your quadratic model, approximate how much was spent on each person in 2008.
Year
Amount, A
(in hours)
2000
3492
2001
3540
2002
3606
2003
3663
2004
3757
2005
3809

171. 36). This table shows the amounts A (in dollars) spent per
36) This table shows the amounts A (in dollars) spent per person on the internet in the United States from 2000 to Use a graphing calculator to create a scatter plot of the data. Let t represent the year, with t = 0 corresponding to 2000.
a) Calculate a quadratic regression line to fit the data. What is its equation?
f(x) = 2.36t t
b) Based on your quadratic model, approximate how much was spent on each person in 2008.
Year
Amount, A
(in hours)
2000
3492
2001
3540
2002
3606
2003
3663
2004
3757
2005
3809