Question 1

Solve.
-$\sqrt { \mathrm { y } - 7 } + 4 = 0$

Accepted Answer

A)  23 
B)  $- 2,2$ 
C)  No solution 
D)  $- 4,4$ 
A)  23 
B)  $- 2,2$ 
C)  No solution 
D)  $- 4,4$

Question 2

Express the number in terms of i.
-$- \sqrt { - 19 }$

Accepted Answer

A)  $\sqrt { 19 \mathrm { i } }$ 
B)  $\sqrt { 19 } \mathrm { i }$ 
C)  $- 19 i$ 
D)  $- \sqrt { 19 } \mathrm { i }$ 
A)  $\sqrt { 19 \mathrm { i } }$ 
B)  $\sqrt { 19 } \mathrm { i }$ 
C)  $- 19 i$ 
D)  $- \sqrt { 19 } \mathrm { i }$

Question 3

Solve by completing the square to obtain exact solutions.
-$$2 x ^ { 2 } + 7 x + 3 = 0$$

Accepted Answer

A)  $- 1,3$ 
B)  $- 3 , - \frac { 1 } { 2 }$ 
C)  $\frac { - 7 \pm 2 \sqrt { 6 } } { 4 }$ 
D)  $\frac { - 4 \pm \sqrt { 3 } } { 2 }$ 
A)  $- 1,3$ 
B)  $- 3 , - \frac { 1 } { 2 }$ 
C)  $\frac { - 7 \pm 2 \sqrt { 6 } } { 4 }$ 
D)  $\frac { - 4 \pm \sqrt { 3 } } { 2 }$

Question 4

Solve.
-$$x ^ { 2 } + 12 x + 36 = 17$$

Accepted Answer

A)  $6 + \sqrt { 17 } , 6 - \sqrt { 17 }$ 
B)  11 
C)  $- 6 + \sqrt { 17 } , - 6 - \sqrt { 17 }$ 
D)  $\sqrt { 17 } , - \sqrt { 17 }$ 
A)  $6 + \sqrt { 17 } , 6 - \sqrt { 17 }$ 
B)  11 
C)  $- 6 + \sqrt { 17 } , - 6 - \sqrt { 17 }$ 
D)  $\sqrt { 17 } , - \sqrt { 17 }$

Question 5

Solve the inequality and graph the solution set.
-$$| x | \geq 7$$

Accepted Answer

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

Question 6

Solve.
-$$\frac { 1 } { t } + \frac { 1 } { 3 t } + \frac { 1 } { 5 t } = 9$$

Accepted Answer

A)  $\frac { 23 } { 135 }$ 
B)  $\frac { 23 } { 45 }$ 
C)  $\frac { 19 } { 135 }$ 
D)  $\frac { 23 } { 27 }$ 
A)  $\frac { 23 } { 135 }$ 
B)  $\frac { 23 } { 45 }$ 
C)  $\frac { 19 } { 135 }$ 
D)  $\frac { 23 } { 27 }$

Question 7

Solve.
-$$8 - | 4 x + 3 | = 5$$

Accepted Answer

A)  $- \frac { 3 } { 2 } , 0$ 
B)  0 
C)  $0 , \frac { 3 } { 2 }$ 
D)  $- \frac { 3 } { 2 } , \frac { 3 } { 2 }$ 
A)  $- \frac { 3 } { 2 } , 0$ 
B)  0 
C)  $0 , \frac { 3 } { 2 }$ 
D)  $- \frac { 3 } { 2 } , \frac { 3 } { 2 }$

Question 8

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

Accepted Answer

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

Question 9

Find the range of the given function.
-$$f ( x ) = - 2 x ^ { 2 } - 12 x - 24$$

Accepted Answer

A)  $( - \infty , - 6 ]$ 
B)  $[ 3 , \infty )$ 
C)  $( - \infty , - 3 ]$ 
D)  $[ 6 , \infty )$ 
A)  $( - \infty , - 6 ]$ 
B)  $[ 3 , \infty )$ 
C)  $( - \infty , - 3 ]$ 
D)  $[ 6 , \infty )$

Question 10

Solve the inequality and graph the solution set.
-$$\left| \frac { 3 x + 6 } { 2 } \right| > 3$$

Accepted Answer

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

Question 11

Simplify.
-$i^{10}$

Accepted Answer

A)  $- \mathrm { i }$ 
B)  1 
C)  $\mathrm { i }$ 
D)  $- 1$ 
A)  $- \mathrm { i }$ 
B)  1 
C)  $\mathrm { i }$ 
D)  $- 1$

Question 12

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$- 6 i ( - 2 + 5 i )$

Accepted Answer

A)  $30 - 12 \mathrm { i }$ 
B)  $12 \mathrm { i } - 30 \mathrm { i } ^ { 2 }$ 
C)  $- 30 - 12 \mathrm { i }$ 
D)  $30 + 12 \mathrm { i }$ 
A)  $30 - 12 \mathrm { i }$ 
B)  $12 \mathrm { i } - 30 \mathrm { i } ^ { 2 }$ 
C)  $- 30 - 12 \mathrm { i }$ 
D)  $30 + 12 \mathrm { i }$

Question 13

Solve and write interval notation for the solution set.
-$| 11 x - 7 | < - 4$

Accepted Answer

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

Question 14

Find the intervals on which the function is increasing and the intervals on which the function is decreasing.
-$$f ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 2 x - \frac { 7 } { 2 }$$

Accepted Answer

A)  Increasing on $( - 5 , \infty )$; decreasing on $( - \infty , - 5 )$ 
B)  Increasing on $( - 1 , \infty )$; decreasing on $( - \infty , - 1 )$ 
C)  Increasing on $( - 1 , \infty )$, decreasing on $( - \infty , - 1 )$ 
D)  Increasing on $( 2 , \infty )$, decreasing on $( - \infty , 2 )$ 
A)  Increasing on $( - 5 , \infty )$; decreasing on $( - \infty , - 5 )$ 
B)  Increasing on $( - 1 , \infty )$; decreasing on $( - \infty , - 1 )$ 
C)  Increasing on $( - 1 , \infty )$, decreasing on $( - \infty , - 1 )$ 
D)  Increasing on $( 2 , \infty )$, decreasing on $( - \infty , 2 )$

Question 15

Solve.
-The length and width of a rectangle have a sum of 84. What dimensions give the maximum area?

Accepted Answer

A) Length 32 and width 52 
B) Length 41 and width 43 
C) Length 42 and width 42 
D) Length 33 and width 51 
A) Length 32 and width 52 
B) Length 41 and width 43 
C) Length 42 and width 42 
D) Length 33 and width 51

Question 16

Match the equation to the correct graph.
-$$y = ( x + 6 ) ^ { 2 }$$

Accepted Answer

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

Question 17

Express the number in terms of i.
-$\sqrt { - 9 }$

Accepted Answer

A)  $\sqrt { 3 } \mathrm { i }$ 
B)  $- \sqrt { 3 } \mathrm { i }$ 
C)  $- 3 \mathrm { i }$ 
D)  $3 \mathrm { i }$ 
A)  $\sqrt { 3 } \mathrm { i }$ 
B)  $- \sqrt { 3 } \mathrm { i }$ 
C)  $- 3 \mathrm { i }$ 
D)  $3 \mathrm { i }$

Question 18

Solve.
-$\sqrt { 10 + x } + \sqrt { 11 - 5 x } = - 1$

Accepted Answer

A)  1 
B)  $\frac { 11 } { 2 }$ 
C)  0 
D)  No solution 
A)  1 
B)  $\frac { 11 } { 2 }$ 
C)  0 
D)  No solution

Question 19

Find the zeros of the function. Give exact answers.
-$$f ( x ) = x ^ { 2 } - 9 x + 3$$

Accepted Answer

A)  $\frac { - 9 \pm \sqrt { 69 } \mathrm { i } } { 2 }$ 
B)  $\frac { 9 \pm \sqrt { 69 } } { 2 }$ 
C)  $\frac { 27 \pm \sqrt { 69 } } { 2 }$ 
D)  $\frac { - 9 \pm \sqrt { 69 } } { 4 }$ 
A)  $\frac { - 9 \pm \sqrt { 69 } \mathrm { i } } { 2 }$ 
B)  $\frac { 9 \pm \sqrt { 69 } } { 2 }$ 
C)  $\frac { 27 \pm \sqrt { 69 } } { 2 }$ 
D)  $\frac { - 9 \pm \sqrt { 69 } } { 4 }$

Question 20

Solve graphically. Round solutions to three decimal places, where appropriate.
-$$3 x ^ { 2 } + 32 x + 14 = 0$$

Accepted Answer

A)  $- 1.77 , - 7.297$ 
B)  $- 0.521 , - 2.146$ 
C)  $- 10.21 , - 0.457$ 
D)  $- 2.395 , - 9.872$ 
A)  $- 1.77 , - 7.297$ 
B)  $- 0.521 , - 2.146$ 
C)  $- 10.21 , - 0.457$ 
D)  $- 2.395 , - 9.872$

Solve. - $\sqrt { \mathrm { y } - 7 } + 4 = 0$

Express the number in terms of i. - $- \sqrt { - 19 }$

Solve by completing the square to obtain exact solutions. - $2 x ^ { 2 } + 7 x + 3 = 0$

Solve. - $x ^ { 2 } + 12 x + 36 = 17$

Solve the inequality and graph the solution set. - $| x | \geq 7$ $Solve the inequality and graph the solution set. - | x | \geq 7$

Solve. - $\frac { 1 } { t } + \frac { 1 } { 3 t } + \frac { 1 } { 5 t } = 9$

Solve. - $8 - | 4 x + 3 | = 5$

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

Find the range of the given function. - $f ( x ) = - 2 x ^ { 2 } - 12 x - 24$

Solve the inequality and graph the solution set. - $\left| \frac { 3 x + 6 } { 2 } \right| > 3$ $Solve the inequality and graph the solution set. - \left| \frac { 3 x + 6 } { 2 } \right| > 3$

Simplify. - $i^{10}$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $- 6 i ( - 2 + 5 i )$

Solve and write interval notation for the solution set. - $| 11 x - 7 | < - 4$

Find the intervals on which the function is increasing and the intervals on which the function is decreasing. - $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 2 x - \frac { 7 } { 2 }$

Solve. -The length and width of a rectangle have a sum of 84. What dimensions give the maximum area?

Match the equation to the correct graph. - $y = ( x + 6 ) ^ { 2 }$

Express the number in terms of i. - $\sqrt { - 9 }$

Solve. - $\sqrt { 10 + x } + \sqrt { 11 - 5 x } = - 1$

Find the zeros of the function. Give exact answers. - $f ( x ) = x ^ { 2 } - 9 x + 3$

Solve graphically. Round solutions to three decimal places, where appropriate. - $3 x ^ { 2 } + 32 x + 14 = 0$

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Exam 3: Quadratic Functions and Equations; Inequalities

Solve. - y−7+4=0\sqrt { \mathrm { y } - 7 } + 4 = 0y−7​+4=0

Express the number in terms of i. - −−19- \sqrt { - 19 }−−19​

Solve by completing the square to obtain exact solutions. - 2x2+7x+3=02 x ^ { 2 } + 7 x + 3 = 02x2+7x+3=0

Solve. - x2+12x+36=17x ^ { 2 } + 12 x + 36 = 17x2+12x+36=17

Solve the inequality and graph the solution set. - ∣x∣≥7| x | \geq 7∣x∣≥7

Solve. - 1t+13t+15t=9\frac { 1 } { t } + \frac { 1 } { 3 t } + \frac { 1 } { 5 t } = 9t1​+3t1​+5t1​=9

Solve. - 8−∣4x+3∣=58 - | 4 x + 3 | = 58−∣4x+3∣=5

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

Find the range of the given function. - f(x)=−2x2−12x−24f ( x ) = - 2 x ^ { 2 } - 12 x - 24f(x)=−2x2−12x−24

Solve the inequality and graph the solution set. - ∣3x+62∣>3\left| \frac { 3 x + 6 } { 2 } \right| > 3​23x+6​​>3

Simplify. - i10i^{10}i10

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - −6i(−2+5i)- 6 i ( - 2 + 5 i )−6i(−2+5i)

Solve and write interval notation for the solution set. - ∣11x−7∣<−4| 11 x - 7 | < - 4∣11x−7∣<−4

Find the intervals on which the function is increasing and the intervals on which the function is decreasing. - f(x)=12x2−2x−72f ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 2 x - \frac { 7 } { 2 }f(x)=21​x2−2x−27​

Solve. -The length and width of a rectangle have a sum of 84. What dimensions give the maximum area?

Match the equation to the correct graph. - y=(x+6)2y = ( x + 6 ) ^ { 2 }y=(x+6)2

Express the number in terms of i. - −9\sqrt { - 9 }−9​

Solve. - 10+x+11−5x=−1\sqrt { 10 + x } + \sqrt { 11 - 5 x } = - 110+x​+11−5x​=−1

Find the zeros of the function. Give exact answers. - f(x)=x2−9x+3f ( x ) = x ^ { 2 } - 9 x + 3f(x)=x2−9x+3

Solve graphically. Round solutions to three decimal places, where appropriate. - 3x2+32x+14=03 x ^ { 2 } + 32 x + 14 = 03x2+32x+14=0

Graphs, Functions, and Models

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Solve. - $\sqrt { \mathrm { y } - 7 } + 4 = 0$

Express the number in terms of i. - $- \sqrt { - 19 }$

Solve by completing the square to obtain exact solutions. - $2 x ^ { 2 } + 7 x + 3 = 0$

Solve. - $x ^ { 2 } + 12 x + 36 = 17$

Solve the inequality and graph the solution set. - $| x | \geq 7$ $Solve the inequality and graph the solution set. - | x | \geq 7$

Solve. - $\frac { 1 } { t } + \frac { 1 } { 3 t } + \frac { 1 } { 5 t } = 9$

Solve. - $8 - | 4 x + 3 | = 5$

Find the range of the given function. - $f ( x ) = - 2 x ^ { 2 } - 12 x - 24$

Solve the inequality and graph the solution set. - $\left| \frac { 3 x + 6 } { 2 } \right| > 3$ $Solve the inequality and graph the solution set. - \left| \frac { 3 x + 6 } { 2 } \right| > 3$

Simplify. - $i^{10}$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $- 6 i ( - 2 + 5 i )$

Solve and write interval notation for the solution set. - $| 11 x - 7 | < - 4$

Find the intervals on which the function is increasing and the intervals on which the function is decreasing. - $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 2 x - \frac { 7 } { 2 }$

Match the equation to the correct graph. - $y = ( x + 6 ) ^ { 2 }$

Express the number in terms of i. - $\sqrt { - 9 }$

Solve. - $\sqrt { 10 + x } + \sqrt { 11 - 5 x } = - 1$

Find the zeros of the function. Give exact answers. - $f ( x ) = x ^ { 2 } - 9 x + 3$

Solve graphically. Round solutions to three decimal places, where appropriate. - $3 x ^ { 2 } + 32 x + 14 = 0$