C Challenge

70. Show that the product of any complex number a + bi and its complex conjugate is a real number.
71. For what real values of x and y is ( x + y i ) 2 open x plus y i , close squared  an imaginary number?
72. Reasoning True or false: The conjugate of the additive inverse of a complex number is equal to the additive inverse of the conjugate of that complex number. Explain your answer.

Standardized Test Prep

SAT/ACT

73. How can you rewrite the expression ( 8 − 5 i ) 2 open 8 minus 5 i , close squared  in the form a + bi?
    1. 39 + 80 i
    2. 39 − 80 i 39 minus 80 i
    3. 69 + 80 i
    4. 69 − 80 i 69 minus 80 i
74. How many solutions does the quadratic equation 4 x 2 − 12 x + 9 = 0 4 x squared , minus 12 x plus 9 equals 0  have?
    6. two real solutions
    7. one real solution
    8. two imaginary solutions
    9. one imaginary solution
75. What are the solutions of 3 x 2 − 2 x − 4 = 0 ? 3 x squared , minus 2 x minus 4 equals 0 question mark
    1. 1 ± 13 3 fraction 1 plus minus square root of 13 , over 3 end fraction
    2. 1 ± i 11 3 fraction 1 plus minus i square root of 11 , over 3 end fraction
    3. − 1 ± 13 3 fraction negative 1 plus minus square root of 13 , over 3 end fraction
    4. − 1 ± i 11 3 fraction negative 1 plus minus i square root of 11 , over 3 end fraction

Short Response

76. Using factoring, what are all four solutions to x 4 − 16 = 0 ? x to the fourth , minus 16 equals 0 question mark  Show your work.

Mixed Review

See Lesson 4-7.

Solve each equation using the Quadratic Formula.

77. 2 x 2 + 3 x − 4 = 0 2 x squared , plus 3 x minus 4 equals 0
78. 4 x 2 + x = 1 4 x squared , plus x equals 1
79. x 2 = − 7 x − 8 x squared , equals negative 7 x minus 8

See Lesson 4-1.

Graph each function. Identify the axis of symmetry.

80. y = − 2 ( x + 1 ) 2 − 3 y equals negative 2 open x plus 1 , close squared , minus 3
81. y = 1 2 ( x − 4 ) 2 + 1 y equals , 1 half , open x minus 4 , close squared , plus 1
82. y = 3 ( x − 1 ) 2 − 5 y equals 3 open x minus 1 , close squared , minus 5

See Lesson 2-3.

Write an equation for each line.

83. m = 3 m equals 3  and the y-intercept is − 4 negative 4
84. m = − 0 . 5 m equals negative 0 . 5  and the y-intercept is − 2 negative 2
85. m = − 7 m equals negative 7  and the y-intercept is 10
86. m = 2 m equals 2  and the y-intercept is 8

Get Ready! To prepare for Lesson 4-9, do Exercises 87–89.

See Lesson 3-3.

Solve each system of inequalities by graphing.

87. { y < 2 x + 4 y ≥ | x − 3 | + 2 left brace . table with 2 rows and 1 column , row1 column 1 , y less than 2 x plus 4 , row2 column 1 , y greater than or equal to absolute value of , x minus 3 , end absolute value , . plus 2 , end table
88. { y > − x y < − | x + 1 | left brace . table with 2 rows and 1 column , row1 column 1 , y greater than negative x , row2 column 1 , y less than negative absolute value of , x plus 1 , end absolute value , , end table
89. { y ≤ | x | + 2 y ≥ − 1 2 x + 4 left brace . table with 2 rows and 1 column , row1 column 1 , y less than or equal to absolute value of x , , plus 2 , row2 column 1 , y greater than or equal to negative , 1 half , x plus 4 , end table

Table of Contents