C Challenge

56. 1. Solve the equation ( x − 7 ) 2 = 0 . open x minus 7 close squared . equals 0 .
    2. Find the vertex of the graph of the related function y = ( x − 7 ) 2 . y equals . open x minus 7 close squared . .
    3. Open-Ended Choose a value for h and repeat parts (a) and (b) using ( x − h ) 2 = 0 open x minus h close squared . equals 0  and y = ( x − h ) 2 . y equals . open x minus h close squared . .
    4. Where would you expect to find the vertex of the graph of y = ( x + 4 ) 2 ? y equals . open x plus 4 close squared . question mark  Explain.

57. Geometry The trapezoid has an area of 1960  cm 2 . 1960 . cm squared , .  Use the formula A = 1 2 h ( b 1 + b 2 ) , eh equals , 1 half , h . open . b sub 1 , plus , b sub 2 . close . comma  where A represents the area of the trapezoid, h represents its height, and b 1 b sub 1  and b 2 b sub 2  represent its bases, to find the value of y.

    

Standardized Test Prep

SAT/ACT

58. A package is shaped like a rectangular prism. The length and the width are equal. The volume of the package is 32  ft 3 . 32 , ft cubed , .  The height is 2 ft. What is its length?
    1. − 4  ft  negative 4 , ft
    2. 4 ft
    3. 8 ft
    4. 16 ft
59. What is the y-intercept of the line with equation y = 3 x − 4 ? y equals 3 x minus 4 question mark
    6. − 4 negative 4
    7. − 3 negative 3
    8. 3
    9. 4
60. What is the domain of the relation { ( 3 , − 1 ) , ( 4 , 2 ) , ( − 2 , 5 ) , ( 1 , 0 ) } ? left brace open 3 comma negative 1 close comma open 4 comma 2 close comma open negative 2 comma 5 close comma open 1 comma 0 close right brace question mark
    1. { − 1 , 0 , 2 , 5 } the set negative 1 comma 0 comma 2 comma 5 end set
    2. { 0 , 2 , 5 } the set 0 comma 2 comma 5 end set
    3. { − 2 , 1 , 3 , 4 } the set negative 2 comma 1 comma 3 comma 4 end set
    4. { 1 , 3 , 4 } the set 1 comma 3 comma 4 end set
61. What is the solution of the inequality − 3 x + 2 ≤ 14 ? negative 3 x plus 2 less than or equal to 14 question mark
    6. x ≤ − 4 x less than or equal to negative 4
    7. x ≥ − 4 x greater than or equal to negative 4
    8. x ≤ 4 x less than or equal to 4
    9. x ≥ 4 x greater than or equal to 4

Extended Response

62. The surface area of a cube is 96  ft 2 . 96 , ft squared , .
    1. What is the length of each edge? Show your work.
    2. Suppose you double the length of each edge. What happens to the surface area of the cube? Show your work.

Mixed Review

See Lesson 9-2.

Graph each function. Label the axis of symmetry and the vertex.

63. y = x 2 + 4 x + 3 y equals . x squared , plus 4 . x plus 3
64. y = x 2 + 5 x + 4 y equals . x squared , plus 5 . x plus 4
65. y = 2 x 2 − 8 x − 5 y equals , 2 x squared , minus 8 x minus 5
66. y = − x 2 + 6 x − 1 y equals negative . x squared , plus 6 . x minus 1
67. y = 6 x 2 − 12 x + 1 y equals , 6 x squared , minus 12 x plus 1
68. y = − 3 x 2 + 18 x y equals negative , 3 x squared , plus 18 x

Get Ready! To prepare for Lesson 9-4, do Exercises 69–74.

See Lesson 8-6.

Factor each expression.

69. 2 c 2 + 29 c + 14 2 c squared , plus 29 c plus 14
70. 3 w 2 + 32 w + 20 3 w squared , plus 32 w plus 20
71. 4 g 2 − 21 g − 18 4 g squared , minus 21 g minus 18
72. 2 r 2 − 13 r − 24 2 r squared , minus 13 r minus 24
73. 3 w 2 + 16 w − 12 3 w squared , plus 16 w minus 12
74. 5 p 2 − 34 p + 24 5 p squared , minus 34 p plus 24

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