Question 1

Use the quadratic formula to solve the equation.
-$$2 y ^ { 2 } - 7 y - 9 = 0$$

Accepted Answer

A)  $\left\{ \frac { 2 } { 9 } , 0 \right\}$ 
B)  $\left\{ \frac { 2 } { 9 } , - 1 \right\}$ 
C)  $\left\{ \frac { 2 } { 9 } , 1 \right\}$ 
D)  $\left\{ \frac { 9 } { 2 } , - 1 \right\}$ 
A)  $\left\{ \frac { 2 } { 9 } , 0 \right\}$ 
B)  $\left\{ \frac { 2 } { 9 } , - 1 \right\}$ 
C)  $\left\{ \frac { 2 } { 9 } , 1 \right\}$ 
D)  $\left\{ \frac { 9 } { 2 } , - 1 \right\}$

Question 2

Find the vertex of the graph of the quadratic function.
-$$f ( x ) = x ^ { 2 } + 14 x - 9$$

Accepted Answer

A)  $( 7,138 )$ 
B)  $( 14,383 )$ 
C)  $( - 7 , - 156 )$ 
D)  $( - 7 , - 58 )$ 
A)  $( 7,138 )$ 
B)  $( 14,383 )$ 
C)  $( - 7 , - 156 )$ 
D)  $( - 7 , - 58 )$

Question 3

Solve the equation by completing the square.
-$$x ^ { 2 } + 4 x + 3 = 0$$

Accepted Answer

A)  $\{ - 1 , - 3 \}$ 
B)  $\{ 1 , - 1 \}$ 
C)  $\{ 6 , - 3 \}$ 
D)  $\{ 1,3 \}$ 
A)  $\{ - 1 , - 3 \}$ 
B)  $\{ 1 , - 1 \}$ 
C)  $\{ 6 , - 3 \}$ 
D)  $\{ 1,3 \}$

Question 4

Solve the inequality. Write the solution set in interval notation.
-$$x ( x + 6 ) ( x - 5 ) > 0$$

Accepted Answer

A)  $( - \infty , - 6 ) \cup ( 0,5 )$ 
B)  $[ - 6,0 ] \cup [ 5 , \infty )$ 
C)  $( - \infty , - 6 ] \cup [ 0,5 ]$ 
D)  $( - 6,0 ) \cup ( 5 , \infty )$ 
A)  $( - \infty , - 6 ) \cup ( 0,5 )$ 
B)  $[ - 6,0 ] \cup [ 5 , \infty )$ 
C)  $( - \infty , - 6 ] \cup [ 0,5 ]$ 
D)  $( - 6,0 ) \cup ( 5 , \infty )$

Question 5

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
-$f ( x ) = ( x + 3 ) ^ { 2 }$

Accepted Answer

A)  Vertex: $( 3,0 )$; axis: $x = 3$
  
B)  Vertex: $( - 3,0 )$; axis: $x = - 3$
  
C)  Vertex: $( 0 , - 3 )$; axis: $x = 0$
  
D)  Vertex: $( 0,3 )$; axis: $x = 0$
  
A)  Vertex: $( 3,0 )$; axis: $x = 3$
  
B)  Vertex: $( - 3,0 )$; axis: $x = - 3$
  
C)  Vertex: $( 0 , - 3 )$; axis: $x = 0$
  
D)  Vertex: $( 0,3 )$; axis: $x = 0$

Question 6

Use the square root property to solve the equation.
$11 x ^ { 2 } = 144$

Accepted Answer

A)  $\left\{ \frac { 12 \sqrt { 11 } } { 11 } \right\}$ 
B)  $\left\{ - \frac { \sqrt { 1584 } } { 11 } , \frac { \sqrt { 1584 } } { 11 } \right\}$ 
C)  $\left\{ - \frac { 12 } { 11 } , \frac { 12 } { 11 } \right\}$ 
D)  $\left\{ - \frac { 12 \sqrt { 11 } } { 11 } , \frac { 12 \sqrt { 11 } } { 11 } \right\}$ 
A)  $\left\{ \frac { 12 \sqrt { 11 } } { 11 } \right\}$ 
B)  $\left\{ - \frac { \sqrt { 1584 } } { 11 } , \frac { \sqrt { 1584 } } { 11 } \right\}$ 
C)  $\left\{ - \frac { 12 } { 11 } , \frac { 12 } { 11 } \right\}$ 
D)  $\left\{ - \frac { 12 \sqrt { 11 } } { 11 } , \frac { 12 \sqrt { 11 } } { 11 } \right\}$

Question 7

Solve the inequality. Write the solution set in interval notation.
-$$\left( x ^ { 2 } - 64 \right) \left( x ^ { 2 } - 25 \right) > 0$$

Accepted Answer

A)  $( - \infty , - 8 ] \cup [ - 5,5 ] \cup [ 8 , \infty )$ 
B)  $( - \infty , - 8 ) \cup ( - 5,5 ) \cup ( 8 , \infty )$ 
C)  $( - 8 , - 5 ) \cup ( 5,8 )$ 
D)  $[ - 8 , - 5 ] \cup [ 5,8 ]$ 
A)  $( - \infty , - 8 ] \cup [ - 5,5 ] \cup [ 8 , \infty )$ 
B)  $( - \infty , - 8 ) \cup ( - 5,5 ) \cup ( 8 , \infty )$ 
C)  $( - 8 , - 5 ) \cup ( 5,8 )$ 
D)  $[ - 8 , - 5 ] \cup [ 5,8 ]$

Question 8

Use the square root property to solve the equation.
$2 x ^ { 2 } + 14 = 0$

Accepted Answer

A)  $\{ - \mathrm { i } \sqrt { 7 } , \mathrm { i } \sqrt { 7 } \}$ 
B)  $\{ - 7 i , 7 i \}$ 
C)  $\{ - \sqrt { 7 } , \sqrt { 7 } \}$ 
D)  $\{ - 7,7 \}$ 
A)  $\{ - \mathrm { i } \sqrt { 7 } , \mathrm { i } \sqrt { 7 } \}$ 
B)  $\{ - 7 i , 7 i \}$ 
C)  $\{ - \sqrt { 7 } , \sqrt { 7 } \}$ 
D)  $\{ - 7,7 \}$

Question 9

Solve the inequality. Write the solution set in interval notation.
-$$\frac { 5 } { x - 1 } < 1$$

Accepted Answer

A)  $( - \infty , 1 )$ 
B)  $( - \infty , 1 ] \cup [ 6 , \infty )$ 
C)  $( - \infty , 1 ) \cup ( 6 , \infty )$ 
D)  $( 1,6 )$ 
A)  $( - \infty , 1 )$ 
B)  $( - \infty , 1 ] \cup [ 6 , \infty )$ 
C)  $( - \infty , 1 ) \cup ( 6 , \infty )$ 
D)  $( 1,6 )$

Question 10

Solve the inequality. Write the solution set in interval notation.
-$$( 2 y + 9 ) ( 4 y - 7 ) \leq 0$$

Accepted Answer

A)  $\left( - \infty , - \frac { 9 } { 2 } \right) \cup \left( \frac { 7 } { 4 } , \infty \right)$ 
B)  $\left( - \frac { 9 } { 2 } , \frac { 7 } { 4 } \right)$ 
C)  $\left[ - \frac { 9 } { 2 } , \frac { 7 } { 4 } \right]$ 
D)  $\left( - \infty , - \frac { 9 } { 2 } \right] \cup \left[ \frac { 7 } { 4 } , \infty \right)$ 
A)  $\left( - \infty , - \frac { 9 } { 2 } \right) \cup \left( \frac { 7 } { 4 } , \infty \right)$ 
B)  $\left( - \frac { 9 } { 2 } , \frac { 7 } { 4 } \right)$ 
C)  $\left[ - \frac { 9 } { 2 } , \frac { 7 } { 4 } \right]$ 
D)  $\left( - \infty , - \frac { 9 } { 2 } \right] \cup \left[ \frac { 7 } { 4 } , \infty \right)$

Question 11

Solve the inequality. Write the solution set in interval notation.
-$$\frac { 5 } { 3 x - 7 } > 0$$

Accepted Answer

A)  $\left( - \infty , \frac { 7 } { 3 } \right)$ 
B)  $( 0 , \infty )$ 
C)  $\left( - \frac { 7 } { 3 } , \infty \right)$ 
D)  $\left( \frac { 7 } { 3 } , \infty \right)$ 
A)  $\left( - \infty , \frac { 7 } { 3 } \right)$ 
B)  $( 0 , \infty )$ 
C)  $\left( - \frac { 7 } { 3 } , \infty \right)$ 
D)  $\left( \frac { 7 } { 3 } , \infty \right)$

Question 12

Use the quadratic formula to solve the equation.
-$$x ^ { 2 } + 16 x + 64 = 0$$

Accepted Answer

A)  $\{ - 8 \}$ 
B)  $\{ 8 - \mathrm { i } , 8 + \mathrm { i } \}$ 
C)  $\{ - 8,8 \}$ 
D)  $\{ 8 \}$ 
A)  $\{ - 8 \}$ 
B)  $\{ 8 - \mathrm { i } , 8 + \mathrm { i } \}$ 
C)  $\{ - 8,8 \}$ 
D)  $\{ 8 \}$

Question 13

Fill in the blank with one of the words or phrases listed below.

-The process of writing a quadratic equation so that one side is a perfect square trinomial is calledـــــــــــــــــ

Accepted Answer

A)  quadratic formula 
B)  completing the square 
C)  quadratic inequality 
D)  discriminant 
A)  quadratic formula 
B)  completing the square 
C)  quadratic inequality 
D)  discriminant

Question 14

Solve the equation by completing the square.
-$$16 x ^ { 2 } - 7 x + 1 = 0$$

Accepted Answer

A)  $\left\{ \frac { 7 - \mathrm { i } \sqrt { 15 } } { 32 } , \frac { - 7 + \mathrm { i } \sqrt { 15 } } { 32 } \right\}$ 
B)  $\left\{ \frac { 7 - i \sqrt { 15 } } { 32 } , \frac { 7 + i \sqrt { 15 } } { 32 } \right\}$ 
C)  $\left\{ \frac { - 7 - \mathrm { i } \sqrt { 15 } } { 32 } , \frac { 7 + \mathrm { i } \sqrt { 15 } } { 32 } \right\}$ 
D)  $\left\{ \frac { - 7 - \mathrm { i } \sqrt { 15 } } { 32 } , \frac { - 7 + \mathrm { i } \sqrt { 15 } } { 32 } \right\}$ 
A)  $\left\{ \frac { 7 - \mathrm { i } \sqrt { 15 } } { 32 } , \frac { - 7 + \mathrm { i } \sqrt { 15 } } { 32 } \right\}$ 
B)  $\left\{ \frac { 7 - i \sqrt { 15 } } { 32 } , \frac { 7 + i \sqrt { 15 } } { 32 } \right\}$ 
C)  $\left\{ \frac { - 7 - \mathrm { i } \sqrt { 15 } } { 32 } , \frac { 7 + \mathrm { i } \sqrt { 15 } } { 32 } \right\}$ 
D)  $\left\{ \frac { - 7 - \mathrm { i } \sqrt { 15 } } { 32 } , \frac { - 7 + \mathrm { i } \sqrt { 15 } } { 32 } \right\}$

Question 15

Solve.
-$x ^ { 4 } - 20 x ^ { 2 } - 576 = 0$

Accepted Answer

A)  $\{ - 6,6 , - 4,4 \}$ 
B)  $\{ - 6,6 , - 4 i , 4 i \}$ 
C)  $\{ - 36,36 , - 16 i , 16 i \}$ 
D)  $\{ - 4,4 , - 6 \mathrm { i } , 6 \mathrm { i } \}$ 
A)  $\{ - 6,6 , - 4,4 \}$ 
B)  $\{ - 6,6 , - 4 i , 4 i \}$ 
C)  $\{ - 36,36 , - 16 i , 16 i \}$ 
D)  $\{ - 4,4 , - 6 \mathrm { i } , 6 \mathrm { i } \}$

Question 16

Use the quadratic formula to solve the equation.
-$$\mathrm { y } ^ { 2 } - 18 \mathrm { y } + 81 = 0$$

Accepted Answer

A)  $\{ - 9,9 \}$ 
B)  $\{ - 9 - i , - 9 + i \}$ 
C)  $\{ - 9 \}$ 
D)  $\{ 9 \}$ 
A)  $\{ - 9,9 \}$ 
B)  $\{ - 9 - i , - 9 + i \}$ 
C)  $\{ - 9 \}$ 
D)  $\{ 9 \}$

Question 17

Solve.
-$$\frac { 1 } { x ^ { 2 } - 11 x + 18 } = \frac { 2 x } { x - 9 } - \frac { x } { x - 2 }$$

Accepted Answer

A)  $\left\{ \frac { 5 - \sqrt { 21 } } { 2 } , \frac { 5 + \sqrt { 21 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 5 - \sqrt { 29 } } { 2 } , \frac { - 5 + \sqrt { 29 } } { 2 } \right\}$ 
C)  $\left\{ \frac { - 5 - \sqrt { 21 } } { 2 } , \frac { - 5 + \sqrt { 21 } } { 2 } \right\}$ 
D)  $\left\{ \frac { 5 - \sqrt { 29 } } { 2 } , \frac { 5 + \sqrt { 29 } } { 2 } \right\}$ 
A)  $\left\{ \frac { 5 - \sqrt { 21 } } { 2 } , \frac { 5 + \sqrt { 21 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 5 - \sqrt { 29 } } { 2 } , \frac { - 5 + \sqrt { 29 } } { 2 } \right\}$ 
C)  $\left\{ \frac { - 5 - \sqrt { 21 } } { 2 } , \frac { - 5 + \sqrt { 21 } } { 2 } \right\}$ 
D)  $\left\{ \frac { 5 - \sqrt { 29 } } { 2 } , \frac { 5 + \sqrt { 29 } } { 2 } \right\}$

Question 18

Solve.
-$$x = 8 + 2 \sqrt { x }$$

Accepted Answer

A)  $\{ 8 \}$ 
B)  $\{ 16 \}$ 
C)  $\{ 32 \}$ 
D)  $\{ 12 \}$ 
A)  $\{ 8 \}$ 
B)  $\{ 16 \}$ 
C)  $\{ 32 \}$ 
D)  $\{ 12 \}$

Question 19

Solve the equation.
-$$\mathrm { n } ^ { 2 } + \mathrm { n } + 7 = 0$$

Accepted Answer

A)  $\left\{ \frac { - 1 - 3 \sqrt { 3 } } { 2 } , \frac { - 1 + 3 \sqrt { 3 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 1 - 3 i \sqrt { 3 } } { 2 } , \frac { - 1 + 3 i \sqrt { 3 } } { 2 } \right\}$ 
C)  $\left\{ \frac { 1 - 3 \sqrt { 3 } } { 2 } , \frac { 1 + 3 \sqrt { 3 } } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 - 3 \mathrm { i } \sqrt { 3 } } { 2 } , \frac { 1 + 3 \mathrm { i } \sqrt { 3 } } { 2 } \right\}$ 
A)  $\left\{ \frac { - 1 - 3 \sqrt { 3 } } { 2 } , \frac { - 1 + 3 \sqrt { 3 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 1 - 3 i \sqrt { 3 } } { 2 } , \frac { - 1 + 3 i \sqrt { 3 } } { 2 } \right\}$ 
C)  $\left\{ \frac { 1 - 3 \sqrt { 3 } } { 2 } , \frac { 1 + 3 \sqrt { 3 } } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 - 3 \mathrm { i } \sqrt { 3 } } { 2 } , \frac { 1 + 3 \mathrm { i } \sqrt { 3 } } { 2 } \right\}$

Question 20

Use the square root property to solve the equation.
$( 4 x - 1 ) ^ { 2 } = \frac { 4 } { 16 }$

Accepted Answer

A)  $\left\{ \frac { 3 } { 8 } , \frac { 1 } { 8 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right\}$ 
C)  $\{ 3 , - 1 \}$ 
D)  $\left\{ - \frac { 1 } { 8 } , \frac { 1 } { 8 } \right\}$ 
A)  $\left\{ \frac { 3 } { 8 } , \frac { 1 } { 8 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right\}$ 
C)  $\{ 3 , - 1 \}$ 
D)  $\left\{ - \frac { 1 } { 8 } , \frac { 1 } { 8 } \right\}$

Use the quadratic formula to solve the equation. - $2 y ^ { 2 } - 7 y - 9 = 0$

Find the vertex of the graph of the quadratic function. - $f ( x ) = x ^ { 2 } + 14 x - 9$

Solve the equation by completing the square. - $x ^ { 2 } + 4 x + 3 = 0$

Solve the inequality. Write the solution set in interval notation. - $x ( x + 6 ) ( x - 5 ) > 0$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f ( x ) = ( x + 3 ) ^ { 2 }$ $Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f ( x ) = ( x + 3 ) ^ { 2 }$

Use the square root property to solve the equation. $11 x ^ { 2 } = 144$

Solve the inequality. Write the solution set in interval notation. - $\left( x ^ { 2 } - 64 \right) \left( x ^ { 2 } - 25 \right) > 0$

Use the square root property to solve the equation. $2 x ^ { 2 } + 14 = 0$

Solve the inequality. Write the solution set in interval notation. - $\frac { 5 } { x - 1 } < 1$

Solve the inequality. Write the solution set in interval notation. - $( 2 y + 9 ) ( 4 y - 7 ) \leq 0$

Solve the inequality. Write the solution set in interval notation. - $\frac { 5 } { 3 x - 7 } > 0$

Use the quadratic formula to solve the equation. - $x ^ { 2 } + 16 x + 64 = 0$

Fill in the blank with one of the words or phrases listed below. -The process of writing a quadratic equation so that one side is a perfect square trinomial is calledـــــــــــــــــ

Solve the equation by completing the square. - $16 x ^ { 2 } - 7 x + 1 = 0$

Solve. - $x ^ { 4 } - 20 x ^ { 2 } - 576 = 0$

Use the quadratic formula to solve the equation. - $\mathrm { y } ^ { 2 } - 18 \mathrm { y } + 81 = 0$

Solve. - $\frac { 1 } { x ^ { 2 } - 11 x + 18 } = \frac { 2 x } { x - 9 } - \frac { x } { x - 2 }$

Solve. - $x = 8 + 2 \sqrt { x }$

Solve the equation. - $\mathrm { n } ^ { 2 } + \mathrm { n } + 7 = 0$

Use the square root property to solve the equation. $( 4 x - 1 ) ^ { 2 } = \frac { 4 } { 16 }$

Real Numbers and Algebraic Expressions

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Exam 8: Quadratic Equations and Functions

Use the quadratic formula to solve the equation. - 2y2−7y−9=02 y ^ { 2 } - 7 y - 9 = 02y2−7y−9=0

Find the vertex of the graph of the quadratic function. - f(x)=x2+14x−9f ( x ) = x ^ { 2 } + 14 x - 9f(x)=x2+14x−9

Solve the equation by completing the square. - x2+4x+3=0x ^ { 2 } + 4 x + 3 = 0x2+4x+3=0

Solve the inequality. Write the solution set in interval notation. - x(x+6)(x−5)>0x ( x + 6 ) ( x - 5 ) > 0x(x+6)(x−5)>0

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=(x+3)2f ( x ) = ( x + 3 ) ^ { 2 }f(x)=(x+3)2

Use the square root property to solve the equation. 11x2=14411 x ^ { 2 } = 14411x2=144

Solve the inequality. Write the solution set in interval notation. - (x2−64)(x2−25)>0\left( x ^ { 2 } - 64 \right) \left( x ^ { 2 } - 25 \right) > 0(x2−64)(x2−25)>0

Use the square root property to solve the equation. 2x2+14=02 x ^ { 2 } + 14 = 02x2+14=0

Solve the inequality. Write the solution set in interval notation. - 5x−1<1\frac { 5 } { x - 1 } < 1x−15​<1

Solve the inequality. Write the solution set in interval notation. - (2y+9)(4y−7)≤0( 2 y + 9 ) ( 4 y - 7 ) \leq 0(2y+9)(4y−7)≤0

Solve the inequality. Write the solution set in interval notation. - 53x−7>0\frac { 5 } { 3 x - 7 } > 03x−75​>0

Use the quadratic formula to solve the equation. - x2+16x+64=0x ^ { 2 } + 16 x + 64 = 0x2+16x+64=0