Find the quadratic function y = a ( x − h ) 2 bold italic y equals bold italic eh open bold italic x minus bold italic h , close squared  whose graph passes through the given points.

64. ( − 2 , 1 ) open negative 2 comma 1 close  and (2, 1)
65. ( − 5 , 2 ) open negative 5 comma 2 close  and ( − 1 , 2 ) open negative 1 comma 2 close
66. ( − 1 , − 4 ) open negative 1 comma negative 4 close  and ( 7 , − 4 ) open 7 comma negative 4 close
67. ( 2 , − 1 ) open 2 comma negative 1 close  and (4, 0)
68. ( − 2 , 18 ) open negative 2 comma 18 close  and (1, 0)
69. ( 1 , − 64 ) open 1 comma negative 64 close  and ( − 3 , 0 ) open negative 3 comma 0 close

Standardized Test Prep

SAT/ACT

70. One parabola below has the equation y = ( x − 4 ) 2 + 2 . y equals open x minus 4 , close squared , plus 2 .  Which equation represents the second parabola?

    

    1. y = − ( x − 4 ) 2 + 2 y equals negative open x minus 4 , close squared , plus 2
    2. y = ( − x − 4 ) 2 + 2 y equals open negative x minus 4 , close squared , plus 2
    3. y = ( x + 4 ) 2 − 2 y equals open x plus 4 , close squared , minus 2

    4. y = − ( x + 4 ) 2 − 2 y equals negative open x plus 4 , close squared , minus 2

71. Which system has the unique solution (1, 4)?
    6. { y = x − 3 x + y = 5 left brace . table with 2 rows and 1 column , row1 column 1 , y equals x minus 3 , row2 column 1 , x plus y equals 5 , end table
    7. { y = − x + 5 x − y = − 3 left brace . table with 2 rows and 1 column , row1 column 1 , y equals negative x plus 5 , row2 column 1 , x minus y equals negative 3 , end table
    8. { x + y = 5 y = − x + 3 left brace . table with 2 rows and 1 column , row1 column 1 , x plus y equals 5 , row2 column 1 , y equals negative x plus 3 , end table
    9. { − x + y = 3 2 x − 2 y = − 6 left brace . table with 2 rows and 2 columns , row1 column 1 , negative x plus y , column 2 equals 3 , row2 column 1 , 2 x minus 2 y , column 2 equals negative 6 , end table
72. What is the formula for the surface area of a right circular cylinder, S = 2 π r h + 2 π r 2 , s equals 2 pi r h plus 2 pi , r squared , comma  solved for h?
    1. h = S 4 π r h equals . fraction s , over 4 pi r end fraction
    2. h = S 2 π r 2 h equals . fraction s , over 2 pi , r squared end fraction
    3. h = S 2 π r − r h equals . fraction s , over 2 pi r end fraction . minus r
    4. h = r − S 2 π r h equals r minus . fraction s , over 2 pi r end fraction

    Short Response

73. An athletic club has 225 feet of fencing to enclose a tennis court. What quadratic function can be used to find the maximum area of the tennis court? Find the maximum area, and the lengths of the sides of the resulting fence.

Mixed Review

See Lesson 3-6.

Solve each system of equations using a matrix.

74. { 3 x − y = 7 2 x + 2 y = 10 left brace . table with 2 rows and 3 columns , row1 column 1 , 3 x minus , column 2 y , column 3 equals 7 , row2 column 1 , 2 x plus , column 2 2 y , column 3 equals 10 , end table
75. { 2 x + 5 y = 10 − 3 x + y = 36 left brace . table with 2 rows and 4 columns , row1 column 1 , 2 x , column 2 plus , column 3 5 y , column 4 equals 10 , row2 column 1 , negative 3 x , column 2 plus , column 3 y , column 4 equals 36 , end table
76. { 3 x + y − 2 z = − 3 x − 3 y − z = − 2 2 x + 2 y + 3 z = 11 left brace . table with 3 rows and 6 columns , row1 column 1 , 3 x , column 2 plus , column 3 y , column 4 minus , column 5 2 z , column 6 equals negative 3 , row2 column 1 , x , column 2 minus , column 3 3 y , column 4 minus , column 5 z , column 6 equals negative 2 , row3 column 1 , 2 x , column 2 plus , column 3 2 y , column 4 plus , column 5 3 z , column 6 equals 11 , end table

See Lesson 2-8.

Graph each inequality.

77. y > 3 x + 1 y greater than , 3 x plus 1
78. y < − x + 4 y less than , minus x plus 4
79. y ≥ 1 2 x − 2 y greater than or equal to , 1 half , x minus 2

See Lesson 2-1.

Determine whether each relation is a function.

80. {(3, 0), ( 2 , − 1 ) , open 2 comma negative 1 close comma  (4, 2)}
81. {(1, 2), (1, 1), ( − 1 , 1 ) open negative 1 comma 1 close }
82. {(1, 2), ( − 1 , 2 ) , ( − 1 , 1 ) open negative 1 comma 2 close comma open negative 1 comma 1 close }

Get Ready! To prepare for Lesson 4-2, do Exercises 83–85.

See Lesson 2-7.

Find the vertex of the graph of each function.

83. y = − 2 | x | y equals negative 2 vertical line x vertical line
84. y = | − x − 1 | y equals vertical line negative x minus 1 vertical line
85. y = 5 | x − 5 | y equals 5 vertical line x minus 5 vertical line

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