Question 1

State whether the function is linear or quadratic.
-$$f ( x ) = 2 x$$

Accepted Answer

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

Question 2

Solve.
-$$\sqrt [ 3 ] { x + 3 } = 4$$

Accepted Answer

A)  64 
B)  1 
C)  13 
D)  61 
A)  64 
B)  1 
C)  13 
D)  61

Question 3

Find the axis of symmetry of the given function.
-$$f ( x ) = - 2 x ^ { 2 } + 13 x + 4$$

Accepted Answer

A)  $x = - \frac { 13 } { 2 }$ 
B)  $x = - \frac { 13 } { 4 }$ 
C)  $x = \frac { 13 } { 4 }$ 
D)  $x = \frac { 13 } { 2 }$ 
A)  $x = - \frac { 13 } { 2 }$ 
B)  $x = - \frac { 13 } { 4 }$ 
C)  $x = \frac { 13 } { 4 }$ 
D)  $x = \frac { 13 } { 2 }$

Question 4

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

Accepted Answer

A)  $( - 7,0 ) , ( 4,0 ) ; - 7,4$ 
B)  $( 4,0 ) , ( 7,0 ) ; 4,7$ 
C)  $( - 4,0 ) , ( 7,0 ) ; - 4,7$ 
D)  $( - 4,0 ) , ( - 7,0 ) ; - 4 , - 7$ 
A)  $( - 7,0 ) , ( 4,0 ) ; - 7,4$ 
B)  $( 4,0 ) , ( 7,0 ) ; 4,7$ 
C)  $( - 4,0 ) , ( 7,0 ) ; - 4,7$ 
D)  $( - 4,0 ) , ( - 7,0 ) ; - 4 , - 7$

Question 5

Solve.
-$$\sqrt [ 3 ] { 2 x - 5 } + 9 = 5$$

Accepted Answer

A)  $- 32$ 
B)  $- \frac { 59 } { 2 }$ 
C)  $\frac { 5 } { 2 }$ 
D)  $- 69$ 
A)  $- 32$ 
B)  $- \frac { 59 } { 2 }$ 
C)  $\frac { 5 } { 2 }$ 
D)  $- 69$

Question 6

Solve.
-$$\sqrt { 3 x + 14 } = x + 3$$

Accepted Answer

A)  0 
B)  $\frac { - 3 \pm \sqrt { 29 } } { 2 }$ 
C)  $\frac { - 3 + \sqrt { 29 } } { 2 }$ 
D)  $\frac { - 3 - \sqrt { 29 } } { 2 }$ 
A)  0 
B)  $\frac { - 3 \pm \sqrt { 29 } } { 2 }$ 
C)  $\frac { - 3 + \sqrt { 29 } } { 2 }$ 
D)  $\frac { - 3 - \sqrt { 29 } } { 2 }$

Question 7

Solve.
-$\sqrt { 3 x + 1 } = 3 + \sqrt { x - 4 }$

Accepted Answer

A)  $- 5 , - 8$ 
B)  5,8 
C)  $- 1$ 
D)  No solution 
A)  $- 5 , - 8$ 
B)  5,8 
C)  $- 1$ 
D)  No solution

Question 8

Solve.
-$$( 4 x - 7 ) ( 4 x - 3 ) = 0$$

Accepted Answer

A)  $- \frac { 7 } { 4 } , - \frac { 3 } { 4 }$ 
B)  $\frac { 7 } { 4 } , \frac { 3 } { 4 }$ 
C)  $\frac { 7 } { 16 } , \frac { 7 } { 16 }$ 
D)  $\frac { 3 } { 8 } , \frac { 9 } { 8 }$ 
A)  $- \frac { 7 } { 4 } , - \frac { 3 } { 4 }$ 
B)  $\frac { 7 } { 4 } , \frac { 3 } { 4 }$ 
C)  $\frac { 7 } { 16 } , \frac { 7 } { 16 }$ 
D)  $\frac { 3 } { 8 } , \frac { 9 } { 8 }$

Question 9

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

Accepted Answer

A)  No solution 
B)  $- 2.6$ 
C) 2 
D)  $2 , - 6$ 
A)  No solution 
B)  $- 2.6$ 
C) 2 
D)  $2 , - 6$

Question 10

Solve.
-$$\frac { 1 } { 5 } + \frac { 5 } { x } = \frac { 1 } { 6 } + \frac { 6 } { x }$$

Accepted Answer

A)  $\frac { 11 } { 30 }$ 
B)  $\frac { 30 } { 11 }$ 
C)  30 
D)  $\frac { 1 } { 30 }$ 
A)  $\frac { 11 } { 30 }$ 
B)  $\frac { 30 } { 11 }$ 
C)  30 
D)  $\frac { 1 } { 30 }$

Question 11

Find the range of the given function.
-$$f ( x ) = 4 x ^ { 2 } - 40 x + 98$$

Accepted Answer

A)  $( - \infty , 2 ]$ 
B)  $[ - 2 , \infty )$ 
C)  $[ 5 , \infty )$ 
D)  $( - \infty , - 5 ]$ 
A)  $( - \infty , 2 ]$ 
B)  $[ - 2 , \infty )$ 
C)  $[ 5 , \infty )$ 
D)  $( - \infty , - 5 ]$

Question 12

Find the vertex of the parabola.
-$$f ( x ) = - x ^ { 2 } + 11 x - 3$$

Accepted Answer

A)  $\left( - \frac { 11 } { 2 } , - \frac { 375 } { 4 } \right)$ 
B)  $( 11 , - 3 )$ 
C)  $\left( \frac { 11 } { 2 } , \frac { 133 } { 4 } \right)$ 
D)  $\left( \frac { 11 } { 2 } , \frac { 109 } { 4 } \right)$ 
A)  $\left( - \frac { 11 } { 2 } , - \frac { 375 } { 4 } \right)$ 
B)  $( 11 , - 3 )$ 
C)  $\left( \frac { 11 } { 2 } , \frac { 133 } { 4 } \right)$ 
D)  $\left( \frac { 11 } { 2 } , \frac { 109 } { 4 } \right)$

Question 13

Determine whether there is a maximum or minimum value for the given function, and find that value.
-$$f ( x ) = - x ^ { 2 } - 8 x - 26$$

Accepted Answer

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

Question 14

Use the quadratic formula to find the exact solutions.
-$$3 x ^ { 2 } - 10 x - 8 = 0$$

Accepted Answer

A)  $- 4 , \frac { 2 } { 3 }$ 
B)  $- \frac { 4 } { 3 } , 8$ 
C)  $- \frac { 2 } { 3 } , 4$ 
D)  $- 2,4$ 
A)  $- 4 , \frac { 2 } { 3 }$ 
B)  $- \frac { 4 } { 3 } , 8$ 
C)  $- \frac { 2 } { 3 } , 4$ 
D)  $- 2,4$

Question 15

Use the graph to find the vertex, the axis of symmetry, and the maximum or minimum value of the function.
-

Accepted Answer

A)  $( 1 , - 3 ) ; x = 1 ;$ minimum: 3 
B)  $( - 3 , - 1 ) ; x = 3 ;$ minimum: 1 
C)  $( 1,3 ) ; x = 1 ;$ minimum: 3 
D)  $( 3,1 ) ; x = 3$; minimum: 1 
A)  $( 1 , - 3 ) ; x = 1 ;$ minimum: 3 
B)  $( - 3 , - 1 ) ; x = 3 ;$ minimum: 1 
C)  $( 1,3 ) ; x = 1 ;$ minimum: 3 
D)  $( 3,1 ) ; x = 3$; minimum: 1

Question 16

Solve.
-$$y ^ { 3 } + 2 y ^ { 2 } - 35 y = 0$$

Accepted Answer

A)  $5 , - 7$ 
B)  $0,5 , - 7$ 
C)  $- 28 , - 7$ 
D)  $0 , - 5,7$ 
A)  $5 , - 7$ 
B)  $0,5 , - 7$ 
C)  $- 28 , - 7$ 
D)  $0 , - 5,7$

Question 17

Simplify. Write your answer in the form a + bi, where a and b are real numbers.
-$$( 7 - \sqrt { - 64 } ) + ( 4 + \sqrt { - 9 } )$$

Accepted Answer

A)  $11 + 5 i$ 
B)  $11 + 11 \mathrm { i }$ 
C)  $11 - 11 \mathrm { i }$ 
D)  $11 - 5 \mathrm { i }$ 
A)  $11 + 5 i$ 
B)  $11 + 11 \mathrm { i }$ 
C)  $11 - 11 \mathrm { i }$ 
D)  $11 - 5 \mathrm { i }$

Question 18

Determine whether there is a maximum or minimum value for the given function, and find that value.
-$$f ( x ) = x ^ { 2 } + 6 x - 1$$

Accepted Answer

A)  Maximum: $- 10$ 
B)  Maximum: 0 
C)  Minimum: $- 3$ 
D)  Minimum: $- 10$ 
A)  Maximum: $- 10$ 
B)  Maximum: 0 
C)  Minimum: $- 3$ 
D)  Minimum: $- 10$

Question 19

Solve.
-$$\frac { 4 } { m + 3 } + \frac { 5 } { m } = \frac { 3 m + 3 } { m ^ { 2 } + 3 m }$$

Accepted Answer

A)  $- 2,12$ 
B)  $- 2$ 
C)  $- 2,2$ 
D)  2 
A)  $- 2,12$ 
B)  $- 2$ 
C)  $- 2,2$ 
D)  2

Question 20

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$( 6 - \sqrt { - 36 } ) ( 2 + \sqrt { - 100 } )$

Accepted Answer

A)  $72 + 48 \mathrm { i }$ 
B)  $72 - 48 \mathrm { i }$ 
C)  $- 72 + 48 i$ 
D)  $3612 + 672 \mathrm { i }$ 
A)  $72 + 48 \mathrm { i }$ 
B)  $72 - 48 \mathrm { i }$ 
C)  $- 72 + 48 i$ 
D)  $3612 + 672 \mathrm { i }$

State whether the function is linear or quadratic. - $f ( x ) = 2 x$

Solve. - $\sqrt [ 3 ] { x + 3 } = 4$

Find the axis of symmetry of the given function. - $f ( x ) = - 2 x ^ { 2 } + 13 x + 4$

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

Solve. - $\sqrt [ 3 ] { 2 x - 5 } + 9 = 5$

Solve. - $\sqrt { 3 x + 14 } = x + 3$

Solve. - $\sqrt { 3 x + 1 } = 3 + \sqrt { x - 4 }$

Solve. - $( 4 x - 7 ) ( 4 x - 3 ) = 0$

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

Solve. - $\frac { 1 } { 5 } + \frac { 5 } { x } = \frac { 1 } { 6 } + \frac { 6 } { x }$

Find the range of the given function. - $f ( x ) = 4 x ^ { 2 } - 40 x + 98$

Find the vertex of the parabola. - $f ( x ) = - x ^ { 2 } + 11 x - 3$

Determine whether there is a maximum or minimum value for the given function, and find that value. - $f ( x ) = - x ^ { 2 } - 8 x - 26$

Use the quadratic formula to find the exact solutions. - $3 x ^ { 2 } - 10 x - 8 = 0$

Use the graph to find the vertex, the axis of symmetry, and the maximum or minimum value of the function. -

Solve. - $y ^ { 3 } + 2 y ^ { 2 } - 35 y = 0$

Simplify. Write your answer in the form a + bi, where a and b are real numbers. - $( 7 - \sqrt { - 64 } ) + ( 4 + \sqrt { - 9 } )$

Determine whether there is a maximum or minimum value for the given function, and find that value. - $f ( x ) = x ^ { 2 } + 6 x - 1$

Solve. - $\frac { 4 } { m + 3 } + \frac { 5 } { m } = \frac { 3 m + 3 } { m ^ { 2 } + 3 m }$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $( 6 - \sqrt { - 36 } ) ( 2 + \sqrt { - 100 } )$

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Exam 3: Quadratic Functions and Equations; Inequalities

State whether the function is linear or quadratic. - f(x)=2xf ( x ) = 2 xf(x)=2x

Solve. - x+33=4\sqrt [ 3 ] { x + 3 } = 43x+3​=4

Find the axis of symmetry of the given function. - f(x)=−2x2+13x+4f ( x ) = - 2 x ^ { 2 } + 13 x + 4f(x)=−2x2+13x+4

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

Solve. - 2x−53+9=5\sqrt [ 3 ] { 2 x - 5 } + 9 = 532x−5​+9=5

Solve. - 3x+14=x+3\sqrt { 3 x + 14 } = x + 33x+14​=x+3

Solve. - 3x+1=3+x−4\sqrt { 3 x + 1 } = 3 + \sqrt { x - 4 }3x+1​=3+x−4​

Solve. - (4x−7)(4x−3)=0( 4 x - 7 ) ( 4 x - 3 ) = 0(4x−7)(4x−3)=0

Solve. - ∣x+2∣=4| x + 2 | = 4∣x+2∣=4

Solve. - 15+5x=16+6x\frac { 1 } { 5 } + \frac { 5 } { x } = \frac { 1 } { 6 } + \frac { 6 } { x }51​+x5​=61​+x6​

Find the range of the given function. - f(x)=4x2−40x+98f ( x ) = 4 x ^ { 2 } - 40 x + 98f(x)=4x2−40x+98

Find the vertex of the parabola. - f(x)=−x2+11x−3f ( x ) = - x ^ { 2 } + 11 x - 3f(x)=−x2+11x−3

Determine whether there is a maximum or minimum value for the given function, and find that value. - f(x)=−x2−8x−26f ( x ) = - x ^ { 2 } - 8 x - 26f(x)=−x2−8x−26

Use the quadratic formula to find the exact solutions. - 3x2−10x−8=03 x ^ { 2 } - 10 x - 8 = 03x2−10x−8=0