Question 1

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

Accepted Answer

A)  $68 - 32 \mathrm { i }$ 
B)  $60 - 32 \mathrm { i }$ 
C)  $68 + 32 \mathrm { i }$ 
D)  $60 + 32 \mathrm { i }$ 
A)  $68 - 32 \mathrm { i }$ 
B)  $60 - 32 \mathrm { i }$ 
C)  $68 + 32 \mathrm { i }$ 
D)  $60 + 32 \mathrm { i }$

Question 2

Solve.
-$$\left| \frac { 1 } { 5 } x - 7 \right| = 4$$

Accepted Answer

A)  55 
B)  15,55 
C)  15 
D)  $15,55,0$ 
A)  55 
B)  15,55 
C)  15 
D)  $15,55,0$

Question 3

Simplify. Write your answer in the form a + bi, where a and b are real numbers.
-$$( - 6 - 4 i ) - ( 5 - i )$$

Accepted Answer

A)  $- 11 + 3 i$ 
B)  $11 + 3 \mathrm { i }$ 
C)  $- 11 - 4 i$ 
D)  $- 11 - 3 i$ 
A)  $- 11 + 3 i$ 
B)  $11 + 3 \mathrm { i }$ 
C)  $- 11 - 4 i$ 
D)  $- 11 - 3 i$

Question 4

Solve.
-A projectile is thrown upward so that its distance above the ground after $t$ seconds is $h ( t ) = - 16 t ^ { 2 } + 420 t$. After how many seconds does it reach its maximum height?

Accepted Answer

A)  $7 \mathrm { sec }$ 
B)  $28 \mathrm { sec }$ 
C)  $21 \mathrm { sec }$ 
D)  $13 \mathrm { sec }$ 
A)  $7 \mathrm { sec }$ 
B)  $28 \mathrm { sec }$ 
C)  $21 \mathrm { sec }$ 
D)  $13 \mathrm { sec }$

Question 5

Match the equation to the correct graph.
-$$y = \frac { 1 } { 2 } ( x - 4 ) ^ { 2 } + 5$$

Accepted Answer

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

Question 6

Solve the problem.
-A stuntman jumps from a rooftop $370 \mathrm { ft }$ off the ground. How long will it take him, falling freely, to reach the ground? (Use the formula s $= 16 \mathrm { t } ^ { 2 }$.)

Accepted Answer

A)  About $11.6 \mathrm { sec }$ 
B)  About $23.1 \mathrm { sec }$ 
C)  About $4.8 \mathrm { sec }$ 
D)  About $76.9 \mathrm { sec }$ 
A)  About $11.6 \mathrm { sec }$ 
B)  About $23.1 \mathrm { sec }$ 
C)  About $4.8 \mathrm { sec }$ 
D)  About $76.9 \mathrm { sec }$

Question 7

Solve.
-The number of mosquitoes $\mathrm { M } ( \mathrm { x } )$, in millions, in a certain area depends on the June rainfall $x$, in inches, according to the function $\mathrm { M } ( \mathrm { x } ) = 3 \mathrm { x } - \mathrm { x } ^ { 2 }$. What rainfall produces the maximum number of mosquitoes?

Accepted Answer

A)  $1.5 \mathrm { in }$. 
B)  $9 \mathrm { in }$. 
C)  $0 \mathrm { in }$. 
D)  3 in. 
A)  $1.5 \mathrm { in }$. 
B)  $9 \mathrm { in }$. 
C)  $0 \mathrm { in }$. 
D)  3 in.

Question 8

Determine whether there is a maximum or minimum value for the given function, and find that value.
-$$f ( x ) = x ^ { 2 } + 2 x - 9$$

Accepted Answer

A)  Maximum: 10 
B)  Minimum: $- 10$ 
C)  Maximum: $- 10$ 
D)  Minimum: 0 
A)  Maximum: 10 
B)  Minimum: $- 10$ 
C)  Maximum: $- 10$ 
D)  Minimum: 0

Question 9

Find the range of the given function.
-$$f ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 8 x - \frac { 5 } { 2 }$$

Accepted Answer

A)  $( - \infty , 0 ]$ 
B)  $\left[ - \infty , - \frac { 53 } { 2 } \right]$ 
C)  $\left[ \frac { 187 } { 2 } , \infty \right)$ 
D)  $\left[ - \frac { 69 } { 2 } , \infty \right]$ 
A)  $( - \infty , 0 ]$ 
B)  $\left[ - \infty , - \frac { 53 } { 2 } \right]$ 
C)  $\left[ \frac { 187 } { 2 } , \infty \right)$ 
D)  $\left[ - \frac { 69 } { 2 } , \infty \right]$

Question 10

Solve the inequality and graph the solution set.
-$$| 5 x + 5 | < - 2$$

Accepted Answer

A) 
  
B)  No solution
  
C) 
  
D) 
  
A) 
  
B)  No solution
  
C) 
  
D)

Question 11

Solve.
-$$( 4 m + 4 ) ^ { 2 } + 8 ( 4 m + 4 ) + 7 = 0$$

Accepted Answer

A)  $- \frac { 5 } { 4 } , - \frac { 11 } { 4 }$ 
B)  $- \frac { 3 } { 4 } , \frac { 3 } { 4 }$ 
C)  $- \frac { 3 } { 4 } , - \frac { 3 } { 4 }$ 
D)  $\frac { 5 } { 4 } , \frac { 11 } { 4 }$ 
A)  $- \frac { 5 } { 4 } , - \frac { 11 } { 4 }$ 
B)  $- \frac { 3 } { 4 } , \frac { 3 } { 4 }$ 
C)  $- \frac { 3 } { 4 } , - \frac { 3 } { 4 }$ 
D)  $\frac { 5 } { 4 } , \frac { 11 } { 4 }$

Question 12

Solve the problem.
-A picture 9 inches by 20 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the mounted
Picture is 476 square inches?

Accepted Answer

A) 4 in. 
B) 6 in. 
C) 6.5 in. 
D) 5 in. 
A) 4 in. 
B) 6 in. 
C) 6.5 in. 
D) 5 in.

Question 13

Find the intervals on which the function is increasing and the intervals on which the function is decreasing.
-$$f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } + 7 x - 8$$

Accepted Answer

A)  Increasing on $\left( - \infty , \frac { 21 } { 11 } \right)$; decreasing on $\left( \frac { 21 } { 11 } , \infty \right)$ 
B)  Increasing on $\left( - \infty , \frac { 21 } { 2 } \right)$; decreasing on $\left( \frac { 21 } { 2 } , \infty \right)$ 
C)  Increasing on $\left( - \infty , \frac { 21 } { 13 } \right) ;$ decreasing on $\left( \frac { 21 } { 13 } , \infty \right)$ 
D)  Increasing on $\left( - \infty , \frac { 21 } { 4 } \right) ;$ decreasing on $\left( \frac { 21 } { 4 } , \infty \right)$ 
A)  Increasing on $\left( - \infty , \frac { 21 } { 11 } \right)$; decreasing on $\left( \frac { 21 } { 11 } , \infty \right)$ 
B)  Increasing on $\left( - \infty , \frac { 21 } { 2 } \right)$; decreasing on $\left( \frac { 21 } { 2 } , \infty \right)$ 
C)  Increasing on $\left( - \infty , \frac { 21 } { 13 } \right) ;$ decreasing on $\left( \frac { 21 } { 13 } , \infty \right)$ 
D)  Increasing on $\left( - \infty , \frac { 21 } { 4 } \right) ;$ decreasing on $\left( \frac { 21 } { 4 } , \infty \right)$

Question 14

Solve graphically. Round solutions to three decimal places, where appropriate.
-$$6 x ^ { 2 } - 15 x + 7 = 0$$

Accepted Answer

A)  $- 0.379,0.879$ 
B)  $0.721,1.979$ 
C)  $1.121,2.379$ 
D)  $0.621,1.879$ 
A)  $- 0.379,0.879$ 
B)  $0.721,1.979$ 
C)  $1.121,2.379$ 
D)  $0.621,1.879$

Question 15

Find the intervals on which the function is increasing and the intervals on which the function is decreasing.
-$$f ( x ) = 2 x ^ { 2 } + 8 x + 6$$

Accepted Answer

A)  Increasing on $( - 4 , \infty )$; decreasing on $( - \infty , - 4 )$ 
B)  Increasing on $( 8 , \infty )$; decreasing on $( - \infty , 8 )$ 
C)  Increasing on $( 2 , \infty )$; decreasing on $( - \infty , 2 )$ 
D)  Increasing on $( - 2 , \infty )$; decreasing on $( - \infty , - 2 )$ 
A)  Increasing on $( - 4 , \infty )$; decreasing on $( - \infty , - 4 )$ 
B)  Increasing on $( 8 , \infty )$; decreasing on $( - \infty , 8 )$ 
C)  Increasing on $( 2 , \infty )$; decreasing on $( - \infty , 2 )$ 
D)  Increasing on $( - 2 , \infty )$; decreasing on $( - \infty , - 2 )$

Question 16

Solve.
-$$m ^ { 2 / 5 } + 2 m ^ { 1 / 5 } - 24 = 0$$

Accepted Answer

A)  1024 
B)  $1024 , - 7776$ 
C)  $- 1024,7776$ 
D)  $1,048,576,60,466,176$ 
A)  1024 
B)  $1024 , - 7776$ 
C)  $- 1024,7776$ 
D)  $1,048,576,60,466,176$

Question 17

Find the range of the given function.
-$$f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } + 3 x - 4$$

Accepted Answer

A)  $\left[ \frac { 11 } { 4 } , \infty \right)$ 
B)  $\left[ - \infty , - \frac { 97 } { 4 } \right]$ 
C)  $[ - 4 , \infty )$ 
D)  $\left( - \infty , \frac { 11 } { 4 } \right]$ 
A)  $\left[ \frac { 11 } { 4 } , \infty \right)$ 
B)  $\left[ - \infty , - \frac { 97 } { 4 } \right]$ 
C)  $[ - 4 , \infty )$ 
D)  $\left( - \infty , \frac { 11 } { 4 } \right]$

Question 18

Find the range of the given function.
-$$f ( x ) = x ^ { 2 } - 3 x + 2$$

Accepted Answer

A)  $\left[ - \infty , \frac { 1 } { 4 } \right]$ 
B)  $\left[ - \frac { 1 } { 4 } , \infty \right]$ 
C)  $\left[ - \infty , \frac { 35 } { 4 } \right]$ 
D)  $\left[ \frac { 35 } { 4 } , \infty \right)$ 
A)  $\left[ - \infty , \frac { 1 } { 4 } \right]$ 
B)  $\left[ - \frac { 1 } { 4 } , \infty \right]$ 
C)  $\left[ - \infty , \frac { 35 } { 4 } \right]$ 
D)  $\left[ \frac { 35 } { 4 } , \infty \right)$

Question 19

Solve.
-$$x ^ { 2 } + 2 x - 48 = 0$$

Accepted Answer

A)  $- 40 , - 8$ 
B)  $\sqrt { - 48 } , - \sqrt { - 48 }$ 
C)  $- 6,8$ 
D)  $6 , - 8$ 
A)  $- 40 , - 8$ 
B)  $\sqrt { - 48 } , - \sqrt { - 48 }$ 
C)  $- 6,8$ 
D)  $6 , - 8$

Question 20

Solve.
-$$\sqrt [ 5 ] { 6 x + 7 } = 3$$

Accepted Answer

A)  243 
B)  $\frac { 118 } { 3 }$ 
C)  $\frac { 81 } { 2 }$ 
D)  236 
A)  243 
B)  $\frac { 118 } { 3 }$ 
C)  $\frac { 81 } { 2 }$ 
D)  236

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

Solve. - $\left| \frac { 1 } { 5 } x - 7 \right| = 4$

Simplify. Write your answer in the form a + bi, where a and b are real numbers. - $( - 6 - 4 i ) - ( 5 - i )$

Solve. -A projectile is thrown upward so that its distance above the ground after $t$ seconds is $h ( t ) = - 16 t ^ { 2 } + 420 t$ . After how many seconds does it reach its maximum height?

Match the equation to the correct graph. - $y = \frac { 1 } { 2 } ( x - 4 ) ^ { 2 } + 5$

Solve the problem. -A stuntman jumps from a rooftop $370 \mathrm { ft }$ off the ground. How long will it take him, falling freely, to reach the ground? (Use the formula s $= 16 \mathrm { t } ^ { 2 }$ .)

Determine whether there is a maximum or minimum value for the given function, and find that value. - $f ( x ) = x ^ { 2 } + 2 x - 9$

Find the range of the given function. - $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 8 x - \frac { 5 } { 2 }$

Solve the inequality and graph the solution set. - $| 5 x + 5 | < - 2$

Solve. - $( 4 m + 4 ) ^ { 2 } + 8 ( 4 m + 4 ) + 7 = 0$

Solve the problem. -A picture 9 inches by 20 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the mounted Picture is 476 square inches?

Find the intervals on which the function is increasing and the intervals on which the function is decreasing. - $f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } + 7 x - 8$

Solve graphically. Round solutions to three decimal places, where appropriate. - $6 x ^ { 2 } - 15 x + 7 = 0$

Find the intervals on which the function is increasing and the intervals on which the function is decreasing. - $f ( x ) = 2 x ^ { 2 } + 8 x + 6$

Solve. - $m ^ { 2 / 5 } + 2 m ^ { 1 / 5 } - 24 = 0$

Find the range of the given function. - $f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } + 3 x - 4$

Find the range of the given function. - $f ( x ) = x ^ { 2 } - 3 x + 2$

Solve. - $x ^ { 2 } + 2 x - 48 = 0$

Solve. - $\sqrt [ 5 ] { 6 x + 7 } = 3$

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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. - (8+2i)2( 8 + 2 \mathrm { i } ) ^ { 2 }(8+2i)2

Solve. - ∣15x−7∣=4\left| \frac { 1 } { 5 } x - 7 \right| = 4​51​x−7​=4

Simplify. Write your answer in the form a + bi, where a and b are real numbers. - (−6−4i)−(5−i)( - 6 - 4 i ) - ( 5 - i )(−6−4i)−(5−i)

Solve. -A projectile is thrown upward so that its distance above the ground after ttt seconds is h(t)=−16t2+420th ( t ) = - 16 t ^ { 2 } + 420 th(t)=−16t2+420t . After how many seconds does it reach its maximum height?

Match the equation to the correct graph. - y=12(x−4)2+5y = \frac { 1 } { 2 } ( x - 4 ) ^ { 2 } + 5y=21​(x−4)2+5

Solve the problem. -A stuntman jumps from a rooftop 370ft370 \mathrm { ft }370ft off the ground. How long will it take him, falling freely, to reach the ground? (Use the formula s =16t2= 16 \mathrm { t } ^ { 2 }=16t2 .)

Determine whether there is a maximum or minimum value for the given function, and find that value. - f(x)=x2+2x−9f ( x ) = x ^ { 2 } + 2 x - 9f(x)=x2+2x−9

Find the range of the given function. - f(x)=12x2−8x−52f ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 8 x - \frac { 5 } { 2 }f(x)=21​x2−8x−25​

Solve the inequality and graph the solution set. - ∣5x+5∣<−2| 5 x + 5 | < - 2∣5x+5∣<−2

Solve. - (4m+4)2+8(4m+4)+7=0( 4 m + 4 ) ^ { 2 } + 8 ( 4 m + 4 ) + 7 = 0(4m+4)2+8(4m+4)+7=0