Question 1

Find the vertex of the parabola.
-$$f ( x ) = - 2 x ^ { 2 } + 5 x + 1$$

Accepted Answer

A)  $\left( \frac { 5 } { 4 } , \frac { 33 } { 8 } \right)$ 
B)  $\left( - \frac { 5 } { 4 } , - \frac { 83 } { 8 } \right)$ 
C)  $\left( - \frac { 5 } { 4 } , - \frac { 67 } { 8 } \right)$ 
D)  $\left( \frac { 5 } { 2 } , \frac { 33 } { 8 } \right)$ 
A)  $\left( \frac { 5 } { 4 } , \frac { 33 } { 8 } \right)$ 
B)  $\left( - \frac { 5 } { 4 } , - \frac { 83 } { 8 } \right)$ 
C)  $\left( - \frac { 5 } { 4 } , - \frac { 67 } { 8 } \right)$ 
D)  $\left( \frac { 5 } { 2 } , \frac { 33 } { 8 } \right)$

Question 2

Use the quadratic formula to find the exact solutions.
-$$x ^ { 2 } + 35 = 5 x$$

Accepted Answer

A)  $\frac { 5 } { 2 } \pm \frac { \sqrt { 115 } } { 2 } \mathrm { i }$ 
B)  0,5 
C)  $- 5,5$ 
D)  $\frac { 5 } { 2 } \pm \frac { 5 } { 2 } \mathrm { i }$ 
A)  $\frac { 5 } { 2 } \pm \frac { \sqrt { 115 } } { 2 } \mathrm { i }$ 
B)  0,5 
C)  $- 5,5$ 
D)  $\frac { 5 } { 2 } \pm \frac { 5 } { 2 } \mathrm { i }$

Question 3

Solve.
-$\mathrm { Z } = \mathrm { A } ( 1 + \mathrm { x } ) ^ { 1 / 3 }$, for $\mathrm { x }$

Accepted Answer

A)  $x = \left( \frac { Z } { A } \right) ^ { 3 }$ 
B)  $x = \left( \frac { A } { Z } \right) ^ { 3 }$ 
C)  $x = \left( \frac { Z } { A } \right) ^ { 3 } + 1$ 
D)  $x = \left( \frac { Z } { A } \right) ^ { 3 } - 1$ 
A)  $x = \left( \frac { Z } { A } \right) ^ { 3 }$ 
B)  $x = \left( \frac { A } { Z } \right) ^ { 3 }$ 
C)  $x = \left( \frac { Z } { A } \right) ^ { 3 } + 1$ 
D)  $x = \left( \frac { Z } { A } \right) ^ { 3 } - 1$

Question 4

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$$( 6 + \sqrt { - 9 } ) ( 2 + \sqrt { - 64 } )$$

Accepted Answer

A)  $588 + 402 \mathrm { i }$ 
B)  $- 12 + 54 i$ 
C)  90 
D)  $90 \mathrm { i }$ 
A)  $588 + 402 \mathrm { i }$ 
B)  $- 12 + 54 i$ 
C)  90 
D)  $90 \mathrm { i }$

Question 5

Solve.
-$$| 8 x | = 2$$

Accepted Answer

A)  $- \frac { 1 } { 4 } , \frac { 1 } { 4 }$ 
B)  $- 4,4$ 
C)  $- \frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 4 }$ 
A)  $- \frac { 1 } { 4 } , \frac { 1 } { 4 }$ 
B)  $- 4,4$ 
C)  $- \frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 4 }$

Question 6

Find the axis of symmetry of the given function.
-$$f ( x ) = - x ^ { 2 } + 7 x - 5$$

Accepted Answer

A)  $x = 7$ 
B)  $x = \frac { 7 } { 8 }$ 
C)  $x = - \frac { 7 } { 2 }$ 
D)  $x = \frac { 7 } { 2 }$ 
A)  $x = 7$ 
B)  $x = \frac { 7 } { 8 }$ 
C)  $x = - \frac { 7 } { 2 }$ 
D)  $x = \frac { 7 } { 2 }$

Question 7

Simplify. Write your answer in the form a + bi, where a and b are real numbers.
-$$( 14 + 8 \mathrm { i } ) - ( 3 + 2 \mathrm { i } )$$

Accepted Answer

A)  $11 + 6 i$ 
B)  $- 17 - 10 \mathrm { i }$ 
C)  $17 - 6 i$ 
D)  $17 + 10 \mathrm { i }$ 
A)  $11 + 6 i$ 
B)  $- 17 - 10 \mathrm { i }$ 
C)  $17 - 6 i$ 
D)  $17 + 10 \mathrm { i }$

Question 8

Express the number in terms of i.
-$- \sqrt { - 75 }$

Accepted Answer

A)  $- 3 \sqrt { 5 } \mathrm { i }$ 
B)  $- 15 \mathrm { i }$ 
C)  $- 5 \sqrt { 3 } \mathrm { i }$ 
D)  $5 \sqrt { 3 } \mathrm { i }$ 
A)  $- 3 \sqrt { 5 } \mathrm { i }$ 
B)  $- 15 \mathrm { i }$ 
C)  $- 5 \sqrt { 3 } \mathrm { i }$ 
D)  $5 \sqrt { 3 } \mathrm { i }$

Question 9

Solve.
-$$30 = \left( \mathrm { m } ^ { 2 } + 7 \mathrm {~m} \right) ^ { 2 } + \left( \mathrm { m } ^ { 2 } + 7 \mathrm {~m} \right)$$

Accepted Answer

A)  $6 , - 1 , \frac { - 7 - \sqrt { 69 } } { 2 } , \frac { - 7 + \sqrt { 69 } } { 2 }$ 
B)  $- 6 , - 1$ 
C)  $- 6 , - 1 , \frac { - 7 - \sqrt { 69 } } { 2 } , \frac { - 7 + \sqrt { 69 } } { 2 }$ 
D)  $- 4 , - 1 , \frac { - 7 - \sqrt { 69 } i } { 2 } , \frac { - 7 + \sqrt { 69 } i } { 2 }$ 
A)  $6 , - 1 , \frac { - 7 - \sqrt { 69 } } { 2 } , \frac { - 7 + \sqrt { 69 } } { 2 }$ 
B)  $- 6 , - 1$ 
C)  $- 6 , - 1 , \frac { - 7 - \sqrt { 69 } } { 2 } , \frac { - 7 + \sqrt { 69 } } { 2 }$ 
D)  $- 4 , - 1 , \frac { - 7 - \sqrt { 69 } i } { 2 } , \frac { - 7 + \sqrt { 69 } i } { 2 }$

Question 10

Find the intervals on which the function is increasing and the intervals on which the function is decreasing.
-f(x)= -x2 + 10x + 24

Accepted Answer

A) Increasing on (- 5, ); decreasing on (- , - 5) 
B) Increasing on (- , 5); decreasing on (5, ) 
C) Increasing on (- , - 5); decreasing on (- 5, ) 
D) Increasing on (5, ); decreasing on (- , 5) 
A) Increasing on (- 5, ); decreasing on (- , - 5) 
B) Increasing on (- , 5); decreasing on (5, ) 
C) Increasing on (- , - 5); decreasing on (- 5, ) 
D) Increasing on (5, ); decreasing on (- , 5)

Question 11

Solve graphically. Round solutions to three decimal places, where appropriate.
-$$3 \mathrm { x } + 1 = 5 \mathrm { x } ^ { 2 }$$

Accepted Answer

A)  $- 0.939,0.139$ 
B)  $0.861,1.939$ 
C)  $- 0.239,0.839$ 
D)  $0.461,1.539$ 
A)  $- 0.939,0.139$ 
B)  $0.861,1.939$ 
C)  $- 0.239,0.839$ 
D)  $0.461,1.539$

Question 12

Solve the problem.
-A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 15 feet by 21 feet and the area of the rug is 216 square feet, how wide will the border be?

Accepted Answer

A) 1.5 ft 
B) 4 ft 
C) 3.5 ft 
D) 2.5 ft 
A) 1.5 ft 
B) 4 ft 
C) 3.5 ft 
D) 2.5 ft

Question 13

Solve.
-$$| x - 2 | - 2 = 4$$

Accepted Answer

A)  $- 8,4$ 
B)  8 
C)  No solution 
D)  $- 4,8$ 
A)  $- 8,4$ 
B)  8 
C)  No solution 
D)  $- 4,8$

Question 14

Solve.
-$\frac { 1 } { \mathrm {~A} } = \frac { 1 } { \mathrm {~m} } + \frac { 1 } { \mathrm { t } }$, for $\mathrm { t }$

Accepted Answer

A)  $t = 2 - \frac { m A } { m - A }$ 
B)  $t = 1 + \frac { m A } { m - A }$ 
C)  $t = \frac { m A } { m - A }$ 
D)  $t = \frac { \mathrm { m } - \mathrm { A } } { \mathrm { mA } }$ 
A)  $t = 2 - \frac { m A } { m - A }$ 
B)  $t = 1 + \frac { m A } { m - A }$ 
C)  $t = \frac { m A } { m - A }$ 
D)  $t = \frac { \mathrm { m } - \mathrm { A } } { \mathrm { mA } }$

Question 15

Use a graphing calculator to find the zeros of the function. Round to three decimal places.
-$$f ( x ) = x ^ { 2 } - 6 x - 5$$

Accepted Answer

A)  $- 0.500,6.500$ 
B)  $- 6.500,0.500$ 
C)  $- 6.742,0.742$ 
D)  $- 0.742,6.742$ 
A)  $- 0.500,6.500$ 
B)  $- 6.500,0.500$ 
C)  $- 6.742,0.742$ 
D)  $- 0.742,6.742$

Question 16

Simplify.
-$\mathrm { i } ^ { 32 }$

Accepted Answer

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

Question 17

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.
-$$3 x ^ { 2 } = 2 x - 4$$

Accepted Answer

A)  One real solution 
B)  Two different real-number solutions 
C)  Two different imaginary-number solutions 
A)  One real solution 
B)  Two different real-number solutions 
C)  Two different imaginary-number solutions

Question 18

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$$( 6 + 6 i ) ( 6 + 4 i )$$

Accepted Answer

A)  $60 + 12 \mathrm { i }$ 
B)  $12 + 60 \mathrm { i }$ 
C)  $12 - 60 \mathrm { i }$ 
D)  $24 \mathrm { i } ^ { 2 } + 60 \mathrm { i } + 36$ 
A)  $60 + 12 \mathrm { i }$ 
B)  $12 + 60 \mathrm { i }$ 
C)  $12 - 60 \mathrm { i }$ 
D)  $24 \mathrm { i } ^ { 2 } + 60 \mathrm { i } + 36$

Question 19

Solve.
-$\sqrt { 10 q - 9 } = 9$

Accepted Answer

A)  81 
B)  $\frac { 81 } { 10 }$ 
C)  9 
D)  $\frac { 36 } { 5 }$ 
A)  81 
B)  $\frac { 81 } { 10 }$ 
C)  9 
D)  $\frac { 36 } { 5 }$

Question 20

Match the equation to the correct graph.
-$$y = 2 ( x - 2 ) ^ { 2 } - 3$$

Accepted Answer

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

Find the vertex of the parabola. - $f ( x ) = - 2 x ^ { 2 } + 5 x + 1$

Use the quadratic formula to find the exact solutions. - $x ^ { 2 } + 35 = 5 x$

Solve. - $\mathrm { Z } = \mathrm { A } ( 1 + \mathrm { x } ) ^ { 1 / 3 }$ , for $\mathrm { x }$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $( 6 + \sqrt { - 9 } ) ( 2 + \sqrt { - 64 } )$

Solve. - $| 8 x | = 2$

Find the axis of symmetry of the given function. - $f ( x ) = - x ^ { 2 } + 7 x - 5$

Simplify. Write your answer in the form a + bi, where a and b are real numbers. - $( 14 + 8 \mathrm { i } ) - ( 3 + 2 \mathrm { i } )$

Express the number in terms of i. - $- \sqrt { - 75 }$

Solve. - $30 = \left( \mathrm { m } ^ { 2 } + 7 \mathrm {~m} \right) ^ { 2 } + \left( \mathrm { m } ^ { 2 } + 7 \mathrm {~m} \right)$

Find the intervals on which the function is increasing and the intervals on which the function is decreasing. -f(x)= -x2 + 10x + 24

Solve graphically. Round solutions to three decimal places, where appropriate. - $3 \mathrm { x } + 1 = 5 \mathrm { x } ^ { 2 }$

Solve the problem. -A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 15 feet by 21 feet and the area of the rug is 216 square feet, how wide will the border be?

Solve. - $| x - 2 | - 2 = 4$

Solve. - $\frac { 1 } { \mathrm {~A} } = \frac { 1 } { \mathrm {~m} } + \frac { 1 } { \mathrm { t } }$ , for $\mathrm { t }$

Use a graphing calculator to find the zeros of the function. Round to three decimal places. - $f ( x ) = x ^ { 2 } - 6 x - 5$

Simplify. - $\mathrm { i } ^ { 32 }$

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. - $3 x ^ { 2 } = 2 x - 4$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $( 6 + 6 i ) ( 6 + 4 i )$

Solve. - $\sqrt { 10 q - 9 } = 9$

Match the equation to the correct graph. - $y = 2 ( x - 2 ) ^ { 2 } - 3$

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Exam 3: Quadratic Functions and Equations; Inequalities

Find the vertex of the parabola. - f(x)=−2x2+5x+1f ( x ) = - 2 x ^ { 2 } + 5 x + 1f(x)=−2x2+5x+1

Use the quadratic formula to find the exact solutions. - x2+35=5xx ^ { 2 } + 35 = 5 xx2+35=5x

Solve. - Z=A(1+x)1/3\mathrm { Z } = \mathrm { A } ( 1 + \mathrm { x } ) ^ { 1 / 3 }Z=A(1+x)1/3 , for x\mathrm { x }x

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - (6+−9)(2+−64)( 6 + \sqrt { - 9 } ) ( 2 + \sqrt { - 64 } )(6+−9​)(2+−64​)

Solve. - ∣8x∣=2| 8 x | = 2∣8x∣=2

Find the axis of symmetry of the given function. - f(x)=−x2+7x−5f ( x ) = - x ^ { 2 } + 7 x - 5f(x)=−x2+7x−5

Simplify. Write your answer in the form a + bi, where a and b are real numbers. - (14+8i)−(3+2i)( 14 + 8 \mathrm { i } ) - ( 3 + 2 \mathrm { i } )(14+8i)−(3+2i)

Express the number in terms of i. - −−75- \sqrt { - 75 }−−75​

Solve. - 30=(m2+7 m)2+(m2+7 m)30 = \left( \mathrm { m } ^ { 2 } + 7 \mathrm {~m} \right) ^ { 2 } + \left( \mathrm { m } ^ { 2 } + 7 \mathrm {~m} \right)30=(m2+7 m)2+(m2+7 m)