C Challenge

Solve for x in terms of a .

76. 2 x 2 − a x = 6 a 2 2 x squared , minus eh x equals , 6 eh squared
77. 3 x 2 + a x = a 2 3 x squared , plus eh x equals , eh squared
78. 2 a 2 x 2 − 8 a x = − 6 2 , eh squared , x squared , minus 8 eh x equals negative 6
79. 4 a 2 x 2 + 8 a x + 3 = 0 4 , eh squared , x squared , plus 8 eh x plus 3 equals 0
80. 3 x 2 + a x 2 = 9 x + 9 a 3 x squared , plus eh , x squared , equals 9 x plus 9 eh
81. 6 a 2 x 2 − 11 a x = 10 6 , eh squared , x squared , minus 11 eh x equals 10
82. Solve x 2 = ( 6 2 ) x + 7 x squared , equals open 6 square root of 2 close x plus 7  by completing the square.

Rewrite each equation in vertex form. Then find the vertex of the graph.

83. y = − 4 x 2 − 5 x + 3 y equals negative 4 , x squared , minus 5 x plus 3
84. y = 1 2 x 2 − 5 x + 12 y equals , 1 half , x squared , minus 5 x plus 12
85. y = − 1 5 x 2 + 4 5 x + 11 5 y equals negative , 1 fifth , x squared , plus , 4 fifths , x plus , 11 over 5

Standardized Test Prep

SAT/ACT

86. The graph of which inequality has its vertex at ( 2 1 2 , − 5 ) ? open . 2 , and 1 half , comma negative 5 . close . question mark
    1. y < | 2 x − 5 | + 5 y less than , vertical line 2 x minus 5 vertical line plus 5
    2. y < | 2 x + 5 | − 5 y less than , vertical line 2 x plus 5 vertical line negative 5
    3. y > | 2 x + 5 | − 5 y greater than , vertical line 2 x plus 5 vertical line negative 5
    4. y > | 2 x − 5 | − 5 y greater than , vertical line 2 x minus 5 vertical line negative 5
87. Which number is a solution of | 9 − x | = 9 + x ? vertical line 9 minus x vertical line equals 9 plus x question mark
    1. − 3 negative 3
    2. 0
    3. 3
    4. 6
88. Joanne tosses an apple seed on the ground. It travels along a parabola with the equation y = − x 2 + 4 . y equals negative , x squared , plus 4 .  Assume the seed was thrown from a height of 4 ft. How many feet away from Joanne will the apple seed land?
    1. 1 ft
    2. 2 ft
    3. 4 ft
    4. 8 ft
    Extended Response
89. List the steps for solving the equation x 2 − 9 = − 8 x x squared , minus 9 equals negative 8 x  by the completing the square method. Explain each step.

Mixed Review

See Problem 4-5.

Solve each equation by factoring. Check your answers.

90. 2 x 2 − 3 x + 1 = 0 2 x squared , minus 3 x plus 1 equals 0
91. x 2 − 4 = − 3 x x squared , minus 4 equals negative 3 x
92. 16 + 22 x = 3 x 2 16 plus 22 x equals , 3 x squared

See Problem 4-3.

Determine whether a quadratic model exists for each set of values. If so, write the model.

93. ( − 4 , 3 ) , ( − 3 , 3 ) , ( − 2 , 4 ) open negative 4 comma 3 close comma open negative 3 comma 3 close comma open negative 2 comma 4 close
94. ( − 1 , 1 2 ) , ( 0 , 2 ) , ( 2 , 2 ) open . negative 1 comma , 1 half . close . comma . open , 0 comma 2 , close . comma . open , 2 comma 2 , close
95. ( 0 , 2 ) , ( 1 , 0 ) , ( 2 , 4 ) open 0 comma 2 close comma open 1 comma 0 close comma open 2 comma 4 close

See Problem 3-2.

Solve each system by elimination.

96. { 2 x + y = 4 3 x − y = 6 left brace . table with 2 rows and 1 column , row1 column 1 , 2 x plus y equals 4 , row2 column 1 , 3 x minus y equals 6 , end table
97. { 2 x + y = 7 − 2 x + 5 y = − 1 left brace . table with 2 rows and 2 columns , row1 column 1 , 2 x plus , column 2 y equals 7 , row2 column 1 , negative 2 x plus , column 2 5 y equals negative 1 , end table
98. { 2 x + 4 y = 10 3 x + 5 y = 14 left brace . table with 2 rows and 1 column , row1 column 1 , 2 x plus 4 y equals 10 , row2 column 1 , 3 x plus 5 y equals 14 , end table

Get Ready! To prepare for Lesson 4-7, do Exercises 99–100.

See Problem 1-3.

Evaluate each expression for the given values of the variables.

99. b 2 − 4 ac ; a = 1 , b = 6 , c = 3 b squared , minus 4 ac semicolon eh equals 1 comma b equals 6 comma c equals 3
100. b 2 − 4 ac ; a = − 5 , b = 2 , c = 4 b squared , minus 4 ac semicolon eh equals negative 5 comma b equals 2 comma c equals 4

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