59. Physics When serving in tennis, a player tosses the tennis ball vertically in the air. The height h of the ball after t seconds is given by the quadratic function h ( t ) = − 5 t 2 + 7 t h open t close equals negative 5 , t squared , plus 7 t  (the height is measured in meters from the point of the toss).
    1. How high in the air does the ball go?
    2. Assume that the player hits the ball on its way down when it's 0.6 m above the point of the toss. For how many seconds is the ball in the air between the toss and the serve?

Standardized Test Prep

SAT/ACT

60. What are the solutions of the equation 6 x 2 + 9 x − 15 = 0 ? 6 x squared , plus 9 x minus 15 equals 0 question mark
    1. 1, − 15 negative 15
    2. 1, − 5 2 negative , 5 halves
    3. − 1 , − 5 negative 1 comma negative 5
    4. 3, 5 2 5 halves
61. The vertex of a parabola is (3, 2). A second point on the parabola is (1, 7). Which point is also on the parabola?
    6. ( − 1 , 7 ) open negative 1 comma 7 close
    7. (3, 7)
    8. (5, 7)
    9. ( 3 , − 2 ) open 3 comma negative 2 close
62. For which quadratic function is − 3 negative 3  the constant term?
    1. y = ( 3 x + 1 ) ( − x − 3 ) y equals open 3 x plus 1 close open negative x minus 3 close
    2. y = x 2 − 3 x + 3 y equals , x squared , minus 3 x plus 3
    3. f ( x ) = ( x − 3 ) ( x − 3 ) f open x close equals open x minus 3 close open x minus 3 close
    4. g ( x ) = − 3 x 2 + 3 x + 9 g open x close equals negative , 3 x squared , plus 3 x plus 9

    Short Response

63. What transformations are needed to go from the parent function f ( x ) = x 2 f open x close equals , x squared  to the new function g ( x ) = − 3 x 2 + 2 ? g open x close equals negative 3 , x squared , plus 2 question mark  Graph g(x).

Mixed Review

See Problem 4-4.

Factor each expression.

64. 16 x 2 − 1 16 x squared , minus 1
65. 5 x 2 − 26 x + 5 5 x squared , minus 26 x plus 5
66. 2 x 2 + 13 x − 7 2 x squared , plus 13 x minus 7

See Lesson 3-5.

Solve each system by elimination. Check your answer.

67. { 7 x − 2 y − 5 z = 24 − x + 3 y + 4 z = − 10 x − y − z = 4 left brace . table with 3 rows and 4 columns , row1 column 1 , 7 x minus , column 2 2 y minus , column 3 5 z equals , column 4 24 , row2 column 1 , negative x plus , column 2 3 y plus , column 3 4 z equals , column 4 negative 10 , row3 column 1 , x minus , column 2 y minus , column 3 z equals , column 4 4 , end table
68. { − 2 x + 9 y − z = 8 3 x − 4 y + z = − 5 5 x + 5 y − z = − 10 left brace . table with 3 rows and 2 columns , row1 column 1 , negative 2 x plus 9 y minus z equals , column 2 8 , row2 column 1 , 3 x minus 4 y plus z equals , column 2 negative 5 , row3 column 1 , 5 x plus 5 y minus z equals , column 2 negative 10 , end table
69. { x − 9 y + 8 z = − 10 x + y − z = 9 − x     − 9 z = 2 left brace . table with 3 rows and 6 columns , row1 column 1 , x , column 2 minus , column 3 9 y , column 4 plus , column 5 8 z equals , column 6 negative 10 , row2 column 1 , x , column 2 plus , column 3 y , column 4 minus , column 5 z equals , column 6 9 , row3 column 1 , negative x , column 2 , column 3 , column 4 minus , column 5 9 z equals , column 6 2 , end table

See Problem 2-7.

Without graphing, identify the vertex, axis of symmetry, and transformations from the parent function f ( x ) = | x | . bold italic f open bold italic x close equals vertical line bold italic x vertical line .

70. y = | x + 9 | + 4 y equals vertical line x plus 9 vertical line plus 4
71. y = | 2 x − 7 | y equals vertical line 2 x minus 7 vertical line
72. y = 3 4 | x | − 1 y equals , 3 fourths , vertical line x vertical line negative 1

Get Ready! To prepare for Lesson 4-6, do Exercises 73–75.

See Lesson 4-4.

Simplify each expression.

73. ( x + 4 ) ( x + 4 ) − 3 open x plus 4 close open x plus 4 close minus 3
74. ( 2 x − 1 ) ( 2 x − 1 ) open 2 x minus 1 close open 2 x minus 1 close
75. ( x − 3 ) ( x − 3 ) open x minus 3 close open x minus 3 close

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