Question 1

Express the number in terms of i.
-$- \sqrt { - 4 }$

Accepted Answer

A)  $2 \mathrm { i }$ 
B)  $- \sqrt { 2 } \mathrm { i }$ 
C)  $- 2 \mathrm { i }$ 
D)  $\sqrt { 2 } \mathrm { i }$ 
A)  $2 \mathrm { i }$ 
B)  $- \sqrt { 2 } \mathrm { i }$ 
C)  $- 2 \mathrm { i }$ 
D)  $\sqrt { 2 } \mathrm { i }$

Question 2

Find the intervals on which the function is increasing and the intervals on which the function is decreasing.
-$$f ( x ) = - 3 x ^ { 2 } + 18 x + 81$$

Accepted Answer

A)  Increasing on $( - 3 , \infty )$; decreasing on $( - \infty , - 3 )$ 
B)  Increasing on $( - \infty , 0 )$; decreasing on $( 0 , - \infty )$ 
C)  Increasing on $( - \infty , 3 )$; decreasing on $( 3 , - \infty )$ 
D)  Increasing on $( - \infty , - 3 )$; decreasing on $( - 3 , - \infty )$ 
A)  Increasing on $( - 3 , \infty )$; decreasing on $( - \infty , - 3 )$ 
B)  Increasing on $( - \infty , 0 )$; decreasing on $( 0 , - \infty )$ 
C)  Increasing on $( - \infty , 3 )$; decreasing on $( 3 , - \infty )$ 
D)  Increasing on $( - \infty , - 3 )$; decreasing on $( - 3 , - \infty )$

Question 3

Solve and write interval notation for the solution set.
-$\left| \frac { 4 x - 1 } { 5 } \right| > 4$

Accepted Answer

A)  $\left( - \infty , - \frac { 25 } { 4 } \right) \cup \left( \frac { 21 } { 4 } , \infty \right)$ 
B)  $\left( - \frac { 25 } { 4 } , \frac { 21 } { 4 } \right)$ 
C)  $\left( - \frac { 19 } { 4 } , \frac { 21 } { 4 } \right)$ 
D)  $\left( - \infty , - \frac { 19 } { 4 } \right) \cup \left( \frac { 21 } { 4 } , \infty \right)$ 
A)  $\left( - \infty , - \frac { 25 } { 4 } \right) \cup \left( \frac { 21 } { 4 } , \infty \right)$ 
B)  $\left( - \frac { 25 } { 4 } , \frac { 21 } { 4 } \right)$ 
C)  $\left( - \frac { 19 } { 4 } , \frac { 21 } { 4 } \right)$ 
D)  $\left( - \infty , - \frac { 19 } { 4 } \right) \cup \left( \frac { 21 } { 4 } , \infty \right)$

Question 4

Consider only the discriminant, $b ^ { 2 } - 4 a c$ to determine whether one real-number solution, two different real-number
solutions, or two different imaginary-number solutions exist.
-$| 5 x | = 0$

Accepted Answer

A)  0,5 
B)  0 
C)  $- 5,5$ 
D)  $- 5,0$ 
A)  0,5 
B)  0 
C)  $- 5,5$ 
D)  $- 5,0$

Question 5

Find the vertex of the parabola.
-$$f ( x ) = - 2 x ^ { 2 } - 20 x - 54$$

Accepted Answer

A)  $( 4,5 )$ 
B)  $( - 5 , - 4 )$ 
C)  $( - 4 , - 5 )$ 
D)  $( 5,4 )$ 
A)  $( 4,5 )$ 
B)  $( - 5 , - 4 )$ 
C)  $( - 4 , - 5 )$ 
D)  $( 5,4 )$

Question 6

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$\frac { \sqrt { 2 } + 8 i } { 3 - 4 i }$

Accepted Answer

A)  $\frac { - 32 + 3 \sqrt { 2 } } { 25 } - \frac { 24 + 4 \sqrt { 2 } } { 25 }$ i 
B)  $\frac { - 32 + 3 \sqrt { 2 } } { 25 }$ 
C)  $\frac { - 32 + 3 \sqrt { 2 } } { 25 } + \frac { 24 + 4 \sqrt { 2 } } { 25 }$ i 
D)  $\frac { 24 + 4 \sqrt { 2 } } { 25 } \mathrm { i }$ 
A)  $\frac { - 32 + 3 \sqrt { 2 } } { 25 } - \frac { 24 + 4 \sqrt { 2 } } { 25 }$ i 
B)  $\frac { - 32 + 3 \sqrt { 2 } } { 25 }$ 
C)  $\frac { - 32 + 3 \sqrt { 2 } } { 25 } + \frac { 24 + 4 \sqrt { 2 } } { 25 }$ i 
D)  $\frac { 24 + 4 \sqrt { 2 } } { 25 } \mathrm { i }$

Question 7

Simplify. Write your answer in the form a + bi, where a and b are real numbers.
-$$( - 8 + 4 \mathrm { i } ) + ( 11 + 4 \mathrm { i } )$$

Accepted Answer

A)  $- 3 + 8 \mathrm { i }$ 
B)  $3 + 8 \mathrm { i }$ 
C)  $3 + 12 \mathrm { i }$ 
D)  $11 + 8 \mathrm { i }$ 
A)  $- 3 + 8 \mathrm { i }$ 
B)  $3 + 8 \mathrm { i }$ 
C)  $3 + 12 \mathrm { i }$ 
D)  $11 + 8 \mathrm { i }$

Question 8

Solve by completing the square to obtain exact solutions.
-$$9 x ^ { 2 } + 27 x + 20 = 0$$

Accepted Answer

A)  $- \frac { 3 } { 4 } , - \frac { 5 } { 3 }$ 
B)  $- \frac { 4 } { 3 } , - \frac { 5 } { 3 }$ 
C)  $\frac { 4 } { 3 } , \frac { 5 } { 3 }$ 
D)  $\frac { 3 } { 4 } , \frac { 3 } { 5 }$ 
A)  $- \frac { 3 } { 4 } , - \frac { 5 } { 3 }$ 
B)  $- \frac { 4 } { 3 } , - \frac { 5 } { 3 }$ 
C)  $\frac { 4 } { 3 } , \frac { 5 } { 3 }$ 
D)  $\frac { 3 } { 4 } , \frac { 3 } { 5 }$

Question 9

Solve.
-$$\frac { 16 } { x ^ { 2 } + 4 x + 16 } = \frac { x } { x - 4 } - \frac { 64 } { x ^ { 3 } - 64 }$$

Accepted Answer

A)  $0 , - 4,4$ 
B)  $0 , - 4$ 
C)  0,4 
D)  0 
A)  $0 , - 4,4$ 
B)  $0 , - 4$ 
C)  0,4 
D)  0

Question 10

Solve and write interval notation for the solution set.
-$$| 4 x | < 3$$

Accepted Answer

A)  $\left( - \infty , \frac { 3 } { 4 } \right)$ 
B)  $\left( - \frac { 3 } { 4 } , \frac { 3 } { 4 } \right)$ 
C)  $\left( - \frac { 4 } { 3 } , \frac { 4 } { 3 } \right)$ 
D)  $\left( - \infty , \frac { 4 } { 3 } \right)$ 
A)  $\left( - \infty , \frac { 3 } { 4 } \right)$ 
B)  $\left( - \frac { 3 } { 4 } , \frac { 3 } { 4 } \right)$ 
C)  $\left( - \frac { 4 } { 3 } , \frac { 4 } { 3 } \right)$ 
D)  $\left( - \infty , \frac { 4 } { 3 } \right)$

Question 11

Solve.
-$\sqrt { x + 6 } + \sqrt { 2 - x } = 4$

Accepted Answer

A)  $\sqrt { 31 } , - 2$ 
B)  0 
C)  $2 , - 2$ 
D)  $- 2$ 
A)  $\sqrt { 31 } , - 2$ 
B)  0 
C)  $2 , - 2$ 
D)  $- 2$

Question 12

Solve the problem.
-The length of a rectangle is three inches more than the width. The area of the rectangle is 304 inches. Find the width of the rectangle.

Accepted Answer

A) 16 in. 
B) 19 in. 
C) 10 in. 
D) 8 in. 
A) 16 in. 
B) 19 in. 
C) 10 in. 
D) 8 in.

Question 13

Solve and write interval notation for the solution set.
-$$| 3 x - 7 | > - 6$$

Accepted Answer

A)  No solution 
B)  $( - \infty , \infty )$ 
C)  $\left( - \infty , \frac { 1 } { 3 } \right) \cup \left( - \frac { 11 } { 3 } , \infty \right)$ 
D)  $\left( - \infty , \frac { 13 } { 3 } \right) \cup \left( \frac { 1 } { 3 } , \infty \right)$ 
A)  No solution 
B)  $( - \infty , \infty )$ 
C)  $\left( - \infty , \frac { 1 } { 3 } \right) \cup \left( - \frac { 11 } { 3 } , \infty \right)$ 
D)  $\left( - \infty , \frac { 13 } { 3 } \right) \cup \left( \frac { 1 } { 3 } , \infty \right)$

Question 14

Find the vertex of the parabola.
-$$f ( x ) = - 3 x ^ { 2 } + 24 x - 51$$

Accepted Answer

A)  $( 4 , - 3 )$ 
B)  $( - 4,3 )$ 
C)  $( - 3,4 )$ 
D)  $( 3 , - 4 )$ 
A)  $( 4 , - 3 )$ 
B)  $( - 4,3 )$ 
C)  $( - 3,4 )$ 
D)  $( 3 , - 4 )$

Question 15

Find the zeros of the function. Give exact answers.
-$$f ( x ) = 2 x ^ { 2 } + 11 x + 3$$

Accepted Answer

A)  $\frac { 11 \pm \sqrt { 115 } } { 4 }$ 
B)  $\frac { - 11 \pm \sqrt { 97 } } { 2 }$ 
C)  $\frac { - 11 \pm \sqrt { 97 } } { 4 }$ 
D)  $\frac { - 11 \pm \sqrt { 115 } } { 2 }$ 
A)  $\frac { 11 \pm \sqrt { 115 } } { 4 }$ 
B)  $\frac { - 11 \pm \sqrt { 97 } } { 2 }$ 
C)  $\frac { - 11 \pm \sqrt { 97 } } { 4 }$ 
D)  $\frac { - 11 \pm \sqrt { 115 } } { 2 }$

Question 16

Simplify.
-$( 4 i ) ^ { 4 }$

Accepted Answer

A)  4 
B)  $4 \mathrm { i }$ 
C)  256 
D)  $256 \mathrm { i }$ 
A)  4 
B)  $4 \mathrm { i }$ 
C)  256 
D)  $256 \mathrm { i }$

Question 17

Find the range of the given function.
-$$f ( x ) = x ^ { 2 } - 14 x + 58$$

Accepted Answer

A)  $[ 7 , \infty )$ 
B)  $( - \infty , 0 ]$ 
C)  $[ - 7 , \infty )$ 
D)  $[ 9 , \infty )$ 
A)  $[ 7 , \infty )$ 
B)  $( - \infty , 0 ]$ 
C)  $[ - 7 , \infty )$ 
D)  $[ 9 , \infty )$

Question 18

Find the zeros of the function. Give exact answers.
-$$f ( x ) = x ^ { 2 } - 5 x - 8$$

Accepted Answer

A)  $\frac { 5 \pm \sqrt { 57 } } { 2 }$ 
B)  $\frac { - 5 \pm \sqrt { 57 } i } { 2 }$ 
C)  $\frac { - 25 \pm \sqrt { 57 } } { 2 }$ 
D)  $\frac { 15 \pm \sqrt { 57 } } { 2 }$ 
A)  $\frac { 5 \pm \sqrt { 57 } } { 2 }$ 
B)  $\frac { - 5 \pm \sqrt { 57 } i } { 2 }$ 
C)  $\frac { - 25 \pm \sqrt { 57 } } { 2 }$ 
D)  $\frac { 15 \pm \sqrt { 57 } } { 2 }$

Question 19

State whether the function is linear or quadratic.
-$$f ( x ) = 5 + 2 x ^ { 2 }$$

Accepted Answer

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

Question 20

Solve.
-$$\frac { x } { x - 5 } - \frac { 5 } { x + 5 } = \frac { 50 } { x ^ { 2 } - 25 }$$

Accepted Answer

A)  $\pm 5$ 
B)  $\frac { 1 } { 5 }$ 
C)  $\pm 5 \mathrm { i }$ 
D)  No solution 
A)  $\pm 5$ 
B)  $\frac { 1 } { 5 }$ 
C)  $\pm 5 \mathrm { i }$ 
D)  No solution

Express the number in terms of i. - $- \sqrt { - 4 }$

Find the intervals on which the function is increasing and the intervals on which the function is decreasing. - $f ( x ) = - 3 x ^ { 2 } + 18 x + 81$

Solve and write interval notation for the solution set. - $\left| \frac { 4 x - 1 } { 5 } \right| > 4$

Consider only the discriminant, $b ^ { 2 } - 4 a c$ to determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist. - $| 5 x | = 0$

Find the vertex of the parabola. - $f ( x ) = - 2 x ^ { 2 } - 20 x - 54$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $\frac { \sqrt { 2 } + 8 i } { 3 - 4 i }$

Simplify. Write your answer in the form a + bi, where a and b are real numbers. - $( - 8 + 4 \mathrm { i } ) + ( 11 + 4 \mathrm { i } )$

Solve by completing the square to obtain exact solutions. - $9 x ^ { 2 } + 27 x + 20 = 0$

Solve. - $\frac { 16 } { x ^ { 2 } + 4 x + 16 } = \frac { x } { x - 4 } - \frac { 64 } { x ^ { 3 } - 64 }$

Solve and write interval notation for the solution set. - $| 4 x | < 3$

Solve. - $\sqrt { x + 6 } + \sqrt { 2 - x } = 4$

Solve the problem. -The length of a rectangle is three inches more than the width. The area of the rectangle is 304 inches. Find the width of the rectangle.

Solve and write interval notation for the solution set. - $| 3 x - 7 | > - 6$

Find the vertex of the parabola. - $f ( x ) = - 3 x ^ { 2 } + 24 x - 51$

Find the zeros of the function. Give exact answers. - $f ( x ) = 2 x ^ { 2 } + 11 x + 3$

Simplify. - $( 4 i ) ^ { 4 }$

Find the range of the given function. - $f ( x ) = x ^ { 2 } - 14 x + 58$

Find the zeros of the function. Give exact answers. - $f ( x ) = x ^ { 2 } - 5 x - 8$

State whether the function is linear or quadratic. - $f ( x ) = 5 + 2 x ^ { 2 }$

Solve. - $\frac { x } { x - 5 } - \frac { 5 } { x + 5 } = \frac { 50 } { x ^ { 2 } - 25 }$

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Exam 3: Quadratic Functions and Equations; Inequalities

Express the number in terms of i. - −−4- \sqrt { - 4 }−−4​

Find the intervals on which the function is increasing and the intervals on which the function is decreasing. - f(x)=−3x2+18x+81f ( x ) = - 3 x ^ { 2 } + 18 x + 81f(x)=−3x2+18x+81

Solve and write interval notation for the solution set. - ∣4x−15∣>4\left| \frac { 4 x - 1 } { 5 } \right| > 4​54x−1​​>4

Consider only the discriminant, b2−4acb ^ { 2 } - 4 a cb2−4ac to determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist. - ∣5x∣=0| 5 x | = 0∣5x∣=0

Find the vertex of the parabola. - f(x)=−2x2−20x−54f ( x ) = - 2 x ^ { 2 } - 20 x - 54f(x)=−2x2−20x−54

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - 2+8i3−4i\frac { \sqrt { 2 } + 8 i } { 3 - 4 i }3−4i2​+8i​

Simplify. Write your answer in the form a + bi, where a and b are real numbers. - (−8+4i)+(11+4i)( - 8 + 4 \mathrm { i } ) + ( 11 + 4 \mathrm { i } )(−8+4i)+(11+4i)

Solve by completing the square to obtain exact solutions. - 9x2+27x+20=09 x ^ { 2 } + 27 x + 20 = 09x2+27x+20=0

Solve. - 16x2+4x+16=xx−4−64x3−64\frac { 16 } { x ^ { 2 } + 4 x + 16 } = \frac { x } { x - 4 } - \frac { 64 } { x ^ { 3 } - 64 }x2+4x+1616​=x−4x​−x3−6464​

Solve and write interval notation for the solution set. - ∣4x∣<3| 4 x | < 3∣4x∣<3

Solve. - x+6+2−x=4\sqrt { x + 6 } + \sqrt { 2 - x } = 4x+6​+2−x​=4