Question 1

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$( 9 - 7 \mathrm { i } ) ( 8 - 5 \mathrm { i } )$

Accepted Answer

A)  $35 \mathrm { i } ^ { 2 } - 101 \mathrm { i } + 72$ 
B)  $107 - 11 \mathrm { i }$ 
C)  $37 + 101 \mathrm { i }$ 
D)  $37 - 101 \mathrm { i }$ 
A)  $35 \mathrm { i } ^ { 2 } - 101 \mathrm { i } + 72$ 
B)  $107 - 11 \mathrm { i }$ 
C)  $37 + 101 \mathrm { i }$ 
D)  $37 - 101 \mathrm { i }$

Question 2

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$$4 \mathrm { i } ( 9 - 4 \mathrm { i } )$$

Accepted Answer

A)  $36 \mathrm { i } - 16 \mathrm { i } ^ { 2 }$ 
B)  $- 16 + 36 i$ 
C)  $16 + 36 \mathrm { i }$ 
D)  $16 - 36 \mathrm { i }$ 
A)  $36 \mathrm { i } - 16 \mathrm { i } ^ { 2 }$ 
B)  $- 16 + 36 i$ 
C)  $16 + 36 \mathrm { i }$ 
D)  $16 - 36 \mathrm { i }$

Question 3

Determine whether there is a maximum or minimum value for the given function, and find that value.
-$$f ( x ) = x ^ { 2 } - 7 x + 6$$

Accepted Answer

A)  Minimum: $- \frac { 25 } { 4 }$ 
B)  Minimum: 11 
C)  Maximum: $\frac { 171 } { 4 }$ 
D)  Minimum: $\frac { 171 } { 4 }$ 
A)  Minimum: $- \frac { 25 } { 4 }$ 
B)  Minimum: 11 
C)  Maximum: $\frac { 171 } { 4 }$ 
D)  Minimum: $\frac { 171 } { 4 }$

Question 4

Use a graphing calculator to find the zeros of the function. Round to three decimal places.
-$$f ( x ) = 5 x ^ { 2 } + 2 x - 1$$

Accepted Answer

A)  $- 0.424,0.824$ 
B)  $- 0.824,0.424$ 
C)  $- 0.290,0.690$ 
D)  $- 0.690,0.290$ 
A)  $- 0.424,0.824$ 
B)  $- 0.824,0.424$ 
C)  $- 0.290,0.690$ 
D)  $- 0.690,0.290$

Question 5

Find the vertex of the parabola.
-$$f ( x ) = x ^ { 2 } - 16 x + 70$$

Accepted Answer

A)  $( 6,0 )$ 
B)  $( 0,8 )$ 
C)  $( 6,8 )$ 
D)  $( 8,6 )$ 
A)  $( 6,0 )$ 
B)  $( 0,8 )$ 
C)  $( 6,8 )$ 
D)  $( 8,6 )$

Question 6

Solve.
-$$9 x ^ { 2 } - 18 x - 16 = 0$$

Accepted Answer

A)  $\frac { 8 } { 9 } , - \frac { 2 } { 9 }$ 
B)  $- \frac { 8 } { 3 } , \frac { 2 } { 3 }$ 
C)  $- \frac { 2 } { 9 } , - \frac { 14 } { 9 }$ 
D)  $\frac { 8 } { 3 } , - \frac { 2 } { 3 }$ 
A)  $\frac { 8 } { 9 } , - \frac { 2 } { 9 }$ 
B)  $- \frac { 8 } { 3 } , \frac { 2 } { 3 }$ 
C)  $- \frac { 2 } { 9 } , - \frac { 14 } { 9 }$ 
D)  $\frac { 8 } { 3 } , - \frac { 2 } { 3 }$

Question 7

Solve.
-$$\frac { 1 } { x - 6 } - \frac { 1 } { x } = \frac { 6 } { x ^ { 2 } - 6 x }$$

Accepted Answer

A)  $\pm \sqrt { 6 } \mathrm { i }$ 
B)  $\pm 6 \mathrm { i }$ 
C)  $\{ x \mid x$ is a real number and $x \neq 0$ and $x \neq 6 \}$ 
D)  No solution 
A)  $\pm \sqrt { 6 } \mathrm { i }$ 
B)  $\pm 6 \mathrm { i }$ 
C)  $\{ x \mid x$ is a real number and $x \neq 0$ and $x \neq 6 \}$ 
D)  No solution

Question 8

Use the given graph to find the x-intercepts and zeros of the function.
-

Accepted Answer

A)  $( - 3,0 ) , ( 5,0 ) ; - 3,5$ 
B)  $( 3,0 ) , ( 5,0 ) ; 3,5$ 
C)  $( - 5,0 ) , ( - 3,0 ) ; - 5 , - 3$ 
D)  $( - 5,0 ) , ( 3,0 ) ; - 5,3$ 
A)  $( - 3,0 ) , ( 5,0 ) ; - 3,5$ 
B)  $( 3,0 ) , ( 5,0 ) ; 3,5$ 
C)  $( - 5,0 ) , ( - 3,0 ) ; - 5 , - 3$ 
D)  $( - 5,0 ) , ( 3,0 ) ; - 5,3$

Question 9

Solve.
-$$x ^ { 2 / 3 } - 7 x ^ { 1 / 3 } + 10 = 0$$

Accepted Answer

A)  $- 8,25$ 
B)  $\pm 1,125$ 
C)  8,125 
D)  $\pm 8 , \pm 125$ 
A)  $- 8,25$ 
B)  $\pm 1,125$ 
C)  8,125 
D)  $\pm 8 , \pm 125$

Question 10

State whether the function is linear or quadratic.
-$$f ( x ) = 4 x ^ { 2 } - 16 x$$

Accepted Answer

A)  Linear 
B)  Quadratic 
A)  Linear 
B)  Quadratic

Question 11

State whether the function is linear or quadratic.
-f(x)= 9x - 4

Accepted Answer

A) Linear 
B) Quadratic 
A) Linear 
B) Quadratic

Question 12

Solve the inequality and graph the solution set.
-$$| x | < 4$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 13

Solve by completing the square to obtain exact solutions.
-$$x ^ { 2 } + 5 x - 5 = 0$$

Accepted Answer

A)  $\frac { - 5 - 3 \sqrt { 5 } } { 2 }$ 
B)  $\frac { - 5 \pm 3 \sqrt { 5 } } { 2 }$ 
C)  $- 5 \pm 3 \sqrt { 5 }$ 
D)  $\frac { 5 + 3 \sqrt { 5 } } { 2 }$ 
A)  $\frac { - 5 - 3 \sqrt { 5 } } { 2 }$ 
B)  $\frac { - 5 \pm 3 \sqrt { 5 } } { 2 }$ 
C)  $- 5 \pm 3 \sqrt { 5 }$ 
D)  $\frac { 5 + 3 \sqrt { 5 } } { 2 }$

Question 14

Solve.
-$$| x | = 3.2$$

Accepted Answer

A)  $- 3.2,3.2$ 
B)  1024 
C)  $- 3.2$ 
D)  $3.2$ 
A)  $- 3.2,3.2$ 
B)  1024 
C)  $- 3.2$ 
D)  $3.2$

Question 15

Solve graphically. Round solutions to three decimal places, where appropriate.
-$$5 x ^ { 2 } - 20 x + 11 = 0$$

Accepted Answer

A)  $1.158,3.842$ 
B)  $- 5.175 , - 2.492$ 
C)  $- 3.675 , - 0.992$ 
D)  $0.658,3.342$ 
A)  $1.158,3.842$ 
B)  $- 5.175 , - 2.492$ 
C)  $- 3.675 , - 0.992$ 
D)  $0.658,3.342$

Question 16

Solve.
-$$9 x ^ { 3 } + x ^ { 2 } - 225 x - 25 = 0$$

Accepted Answer

A)  $- 5,5 , - \frac { 1 } { 9 }$ 
B)  $5 , \frac { 1 } { 9 }$ 
C)  $- 5,5 , - 9$ 
D)  $- 25,25 , - \frac { 1 } { 9 }$ 
A)  $- 5,5 , - \frac { 1 } { 9 }$ 
B)  $5 , \frac { 1 } { 9 }$ 
C)  $- 5,5 , - 9$ 
D)  $- 25,25 , - \frac { 1 } { 9 }$

Question 17

Solve.
-$49 \mathrm { t } ^ { 3 } + 16 \mathrm { t } = - 70 \mathrm { t } ^ { 2 }$

Accepted Answer

A)  $- \frac { 8 } { 49 } , \frac { 24 } { 49 }$ 
B)  $0 , - \frac { 2 } { 7 } , - \frac { 8 } { 7 }$ 
C)  $- \frac { 2 } { 7 } , - \frac { 8 } { 7 }$ 
D)  $0 , \frac { 2 } { 7 } , \frac { 8 } { 7 }$ 
A)  $- \frac { 8 } { 49 } , \frac { 24 } { 49 }$ 
B)  $0 , - \frac { 2 } { 7 } , - \frac { 8 } { 7 }$ 
C)  $- \frac { 2 } { 7 } , - \frac { 8 } { 7 }$ 
D)  $0 , \frac { 2 } { 7 } , \frac { 8 } { 7 }$

Question 18

Use the quadratic formula to find the exact solutions.
-$$x ^ { 2 } + 12 x = - 32$$

Accepted Answer

A)  $- 8,4$ 
B)  4,8 
C)  $- 4 , - 8$ 
D)  $- 4,8$ 
A)  $- 8,4$ 
B)  4,8 
C)  $- 4 , - 8$ 
D)  $- 4,8$

Question 19

Solve.
-A rock falls from a tower that is $160 \mathrm { ft }$ high. As it is falling, its height is given by the function $h ( t ) = 160 - 16 t ^ { 2 }$. How many seconds will it take for the rock to hit the ground $( h = 0 )$ ?

Accepted Answer

A)  $12.6 \mathrm { sec }$ 
B)  $1600 \mathrm { sec }$ 
C)  $10.2 \mathrm { sec }$ 
D)  $3.2 \mathrm { sec }$ 
A)  $12.6 \mathrm { sec }$ 
B)  $1600 \mathrm { sec }$ 
C)  $10.2 \mathrm { sec }$ 
D)  $3.2 \mathrm { sec }$

Question 20

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$$\frac { 2 - 7 i } { 1 + 6 i } + \frac { 3 - 5 i } { 1 + 6 i }$$

Accepted Answer

A)  $\frac { 67 } { 37 } + \frac { 42 } { 37 } \mathrm { i }$ 
B)  $- \frac { 67 } { 37 } + \frac { 42 } { 37 } \mathrm { i }$ 
C)  $\frac { 67 } { 37 } - \frac { 42 } { 37 } \mathrm { i }$ 
D)  $- \frac { 67 } { 37 } - \frac { 42 } { 37 } \mathrm { i }$ 
A)  $\frac { 67 } { 37 } + \frac { 42 } { 37 } \mathrm { i }$ 
B)  $- \frac { 67 } { 37 } + \frac { 42 } { 37 } \mathrm { i }$ 
C)  $\frac { 67 } { 37 } - \frac { 42 } { 37 } \mathrm { i }$ 
D)  $- \frac { 67 } { 37 } - \frac { 42 } { 37 } \mathrm { i }$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $( 9 - 7 \mathrm { i } ) ( 8 - 5 \mathrm { i } )$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $4 \mathrm { i } ( 9 - 4 \mathrm { i } )$

Determine whether there is a maximum or minimum value for the given function, and find that value. - $f ( x ) = x ^ { 2 } - 7 x + 6$

Use a graphing calculator to find the zeros of the function. Round to three decimal places. - $f ( x ) = 5 x ^ { 2 } + 2 x - 1$

Find the vertex of the parabola. - $f ( x ) = x ^ { 2 } - 16 x + 70$

Solve. - $9 x ^ { 2 } - 18 x - 16 = 0$

Solve. - $\frac { 1 } { x - 6 } - \frac { 1 } { x } = \frac { 6 } { x ^ { 2 } - 6 x }$

Use the given graph to find the x-intercepts and zeros of the function. -

Solve. - $x ^ { 2 / 3 } - 7 x ^ { 1 / 3 } + 10 = 0$

State whether the function is linear or quadratic. - $f ( x ) = 4 x ^ { 2 } - 16 x$

State whether the function is linear or quadratic. -f(x)= 9x - 4

Solve the inequality and graph the solution set. - $| x | < 4$

Solve by completing the square to obtain exact solutions. - $x ^ { 2 } + 5 x - 5 = 0$

Solve. - $| x | = 3.2$

Solve graphically. Round solutions to three decimal places, where appropriate. - $5 x ^ { 2 } - 20 x + 11 = 0$

Solve. - $9 x ^ { 3 } + x ^ { 2 } - 225 x - 25 = 0$

Solve. - $49 \mathrm { t } ^ { 3 } + 16 \mathrm { t } = - 70 \mathrm { t } ^ { 2 }$

Use the quadratic formula to find the exact solutions. - $x ^ { 2 } + 12 x = - 32$

Solve. -A rock falls from a tower that is $160 \mathrm { ft }$ high. As it is falling, its height is given by the function $h ( t ) = 160 - 16 t ^ { 2 }$ . How many seconds will it take for the rock to hit the ground $( h = 0 )$ ?

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $\frac { 2 - 7 i } { 1 + 6 i } + \frac { 3 - 5 i } { 1 + 6 i }$

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Exam 3: Quadratic Functions and Equations; Inequalities

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - (9−7i)(8−5i)( 9 - 7 \mathrm { i } ) ( 8 - 5 \mathrm { i } )(9−7i)(8−5i)

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - 4i(9−4i)4 \mathrm { i } ( 9 - 4 \mathrm { i } )4i(9−4i)

Determine whether there is a maximum or minimum value for the given function, and find that value. - f(x)=x2−7x+6f ( x ) = x ^ { 2 } - 7 x + 6f(x)=x2−7x+6

Use a graphing calculator to find the zeros of the function. Round to three decimal places. - f(x)=5x2+2x−1f ( x ) = 5 x ^ { 2 } + 2 x - 1f(x)=5x2+2x−1

Find the vertex of the parabola. - f(x)=x2−16x+70f ( x ) = x ^ { 2 } - 16 x + 70f(x)=x2−16x+70

Solve. - 9x2−18x−16=09 x ^ { 2 } - 18 x - 16 = 09x2−18x−16=0

Solve. - 1x−6−1x=6x2−6x\frac { 1 } { x - 6 } - \frac { 1 } { x } = \frac { 6 } { x ^ { 2 } - 6 x }x−61​−x1​=x2−6x6​