Question 1

Solve by completing the square.
-$$x ^ { 2 } + 16 x = - 43$$

Accepted Answer

A)  $\{ 8 - \sqrt { 43 } , 8 + \sqrt { 43 } \}$ 
B)  $\{ - 16 + \sqrt { 43 } \}$ 
C)  $\{ 8 + \sqrt { 21 } \}$ 
D)  $\{ - 8 - \sqrt { 21 } , - 8 + \sqrt { 21 } \}$ 
A)  $\{ 8 - \sqrt { 43 } , 8 + \sqrt { 43 } \}$ 
B)  $\{ - 16 + \sqrt { 43 } \}$ 
C)  $\{ 8 + \sqrt { 21 } \}$ 
D)  $\{ - 8 - \sqrt { 21 } , - 8 + \sqrt { 21 } \}$

Question 2

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
-$$x ^ { 2 } + 14 x$$

Accepted Answer

A)  $x ^ { 2 } + 14 x + 14 = ( x + 196 ) ^ { 2 }$ 
B)  $x ^ { 2 } + 14 x + 196 = ( x + 14 ) ^ { 2 }$ 
C)  $x ^ { 2 } + 14 x + 49 = ( x + 7 ) ^ { 2 }$ 
D)  $x ^ { 2 } + 14 x + 7 = ( x + 49 ) ^ { 2 }$ 
A)  $x ^ { 2 } + 14 x + 14 = ( x + 196 ) ^ { 2 }$ 
B)  $x ^ { 2 } + 14 x + 196 = ( x + 14 ) ^ { 2 }$ 
C)  $x ^ { 2 } + 14 x + 49 = ( x + 7 ) ^ { 2 }$ 
D)  $x ^ { 2 } + 14 x + 7 = ( x + 49 ) ^ { 2 }$

Question 3

Graph the function. Find and label the vertex, y-intercept, and x-intercepts (if any).

-$F(x)=2 x^{2}-4 x+3$

Accepted Answer

A)  vertex: $( 1,1 )$
$x$-intercept: $( 0,0 ) , y$-intercept: $( 0,3 )$ 
  
B)  vertex: $( 1,1 )$
x-intercept: $( 3,0 )$, y-intercept: none
  
C)  vertex: $( 1,1 )$
$x$-intercept: none, y-intercept: $( 0,3 )$ 
  
D)  vertex: $( 1,1 )$
$x$-intercept: none, y-intercept: $( 0,3 )$ 
  
A)  vertex: $( 1,1 )$
$x$-intercept: $( 0,0 ) , y$-intercept: $( 0,3 )$ 
  
B)  vertex: $( 1,1 )$
x-intercept: $( 3,0 )$, y-intercept: none
  
C)  vertex: $( 1,1 )$
$x$-intercept: none, y-intercept: $( 0,3 )$ 
  
D)  vertex: $( 1,1 )$
$x$-intercept: none, y-intercept: $( 0,3 )$

Question 4

Use the quadratic formula to solve the equation.
-$5 x ^ { 2 } + 7 x + 9 = 0$

Accepted Answer

A)  $\left\{ \frac { - 7 - \sqrt { 131 } } { 10 } , \frac { - 7 + \sqrt { 131 } } { 10 } \right\}$ 
B)  $\left\{ \frac { 7 - \mathrm { i } \sqrt { 131 } } { 10 } , \frac { 7 + \mathrm { i } \sqrt { 131 } } { 10 } \right\}$ 
C)  $\left\{ \frac { - 7 - \mathrm { i } \sqrt { 131 } } { 10 } , \frac { - 7 + \mathrm { i } \sqrt { 131 } } { 10 } \right\}$ 
D)  $\left\{ \frac { 7 - \sqrt { 131 } } { 10 } , \frac { 7 + \sqrt { 131 } } { 10 } \right\}$ 
A)  $\left\{ \frac { - 7 - \sqrt { 131 } } { 10 } , \frac { - 7 + \sqrt { 131 } } { 10 } \right\}$ 
B)  $\left\{ \frac { 7 - \mathrm { i } \sqrt { 131 } } { 10 } , \frac { 7 + \mathrm { i } \sqrt { 131 } } { 10 } \right\}$ 
C)  $\left\{ \frac { - 7 - \mathrm { i } \sqrt { 131 } } { 10 } , \frac { - 7 + \mathrm { i } \sqrt { 131 } } { 10 } \right\}$ 
D)  $\left\{ \frac { 7 - \sqrt { 131 } } { 10 } , \frac { 7 + \sqrt { 131 } } { 10 } \right\}$

Question 5

Match the function with its graph.
-$f ( x ) = x ^ { 2 } - 2 x - 8$

Accepted Answer

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

Question 6

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
-$f ( x ) = - \frac { 1 } { 4 } x ^ { 2 }$

Accepted Answer

A)  Vertex: $( 0,0 )$; axis: $y = 0$
  
B)  Vertex: $( 0,0 )$; axis: $x = 0$
  
C)  Vertex: $( 0,0 ) ;$ axis: $\mathrm { y } = 0$
  
D)  Vertex: $( 0,0 )$; axis: $x = 0$
  
A)  Vertex: $( 0,0 )$; axis: $y = 0$
  
B)  Vertex: $( 0,0 )$; axis: $x = 0$
  
C)  Vertex: $( 0,0 ) ;$ axis: $\mathrm { y } = 0$
  
D)  Vertex: $( 0,0 )$; axis: $x = 0$

Question 7

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
-$f ( x ) = x ^ { 2 } - 5$

Accepted Answer

A)  Vertex: $( - 5,0 )$; axis: $x = - 5$
  
B)  Vertex: $( 0,5 )$; axis: $x = 0$
  
C)  Vertex: $( 5,0 )$; axis: $x = 5$
  
D)  Vertex: $( 0 , - 5 )$; axis: $x = 0$
  
A)  Vertex: $( - 5,0 )$; axis: $x = - 5$
  
B)  Vertex: $( 0,5 )$; axis: $x = 0$
  
C)  Vertex: $( 5,0 )$; axis: $x = 5$
  
D)  Vertex: $( 0 , - 5 )$; axis: $x = 0$

Question 8

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

Accepted Answer

A)  $\{ 2 , - i , i \}$ 
B)  $\{ - 1,1,2 i , - 2 i \}$ 
C)  $\{ - 2 , - i , i \}$ 
D)  $\{ - 1,1,2 , - 2 \}$ 
A)  $\{ 2 , - i , i \}$ 
B)  $\{ - 1,1,2 i , - 2 i \}$ 
C)  $\{ - 2 , - i , i \}$ 
D)  $\{ - 1,1,2 , - 2 \}$

Question 9

Solve.
-The cost in millions of dollars for a company to manufacture $x$ thousand automobiles is given by the function $C ( x ) = 5 x ^ { 2 } - 30 x + 81$. Find the number of automobiles that must be produced to minimize the cost.

Accepted Answer

A)  3 thousand automobiles 
B)  36 thousand automobiles 
C)  15 thousand automobiles 
D)  6 thousand automobiles 
A)  3 thousand automobiles 
B)  36 thousand automobiles 
C)  15 thousand automobiles 
D)  6 thousand automobiles

Question 10

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
-$$x ^ { 2 } + \frac { 1 } { 6 } x$$

Accepted Answer

A)  $x ^ { 2 } + \frac { 1 } { 6 } x + 144 = ( x + 12 ) ^ { 2 }$ 
B)  $x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 144 } = \left( x + \frac { 1 } { 12 } \right) ^ { 2 }$ 
C)  $x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 36 } = \left( x + \frac { 1 } { 6 } \right) ^ { 2 }$ 
D)  $x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 12 } = \left( x + \frac { 1 } { 6 } \right) ^ { 2 }$ 
A)  $x ^ { 2 } + \frac { 1 } { 6 } x + 144 = ( x + 12 ) ^ { 2 }$ 
B)  $x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 144 } = \left( x + \frac { 1 } { 12 } \right) ^ { 2 }$ 
C)  $x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 36 } = \left( x + \frac { 1 } { 6 } \right) ^ { 2 }$ 
D)  $x ^ { 2 } + \frac { 1 } { 6 } x + \frac { 1 } { 12 } = \left( x + \frac { 1 } { 6 } \right) ^ { 2 }$

Question 11

Solve.
-The area of a square porch is 121 square feet. Find the dimensions of the porch.

Accepted Answer

A)  10 feet by 10 feet 
B)  13 feet by 13 feet 
C)  12 feet by 12 feet 
D)  11 feet by 11 feet 
A)  10 feet by 10 feet 
B)  13 feet by 13 feet 
C)  12 feet by 12 feet 
D)  11 feet by 11 feet

Question 12

Use the quadratic formula to solve the equation.
-$$4 x ^ { 2 } + 10 x = - 3$$

Accepted Answer

A)  $\left\{ \frac { - 5 - \sqrt { 13 } } { 8 } , \frac { - 5 + \sqrt { 13 } } { 8 } \right\}$ 
B)  $\left\{ \frac { - 10 - \sqrt { 13 } } { 4 } , \frac { - 10 + \sqrt { 13 } } { 4 } \right\}$ 
C)  $\left\{ \frac { - 5 - \sqrt { 37 } } { 4 } , \frac { - 5 + \sqrt { 37 } } { 4 } \right\}$ 
D)  $\left\{ \frac { - 5 - \sqrt { 13 } } { 4 } , \frac { - 5 + \sqrt { 13 } } { 4 } \right\}$ 
A)  $\left\{ \frac { - 5 - \sqrt { 13 } } { 8 } , \frac { - 5 + \sqrt { 13 } } { 8 } \right\}$ 
B)  $\left\{ \frac { - 10 - \sqrt { 13 } } { 4 } , \frac { - 10 + \sqrt { 13 } } { 4 } \right\}$ 
C)  $\left\{ \frac { - 5 - \sqrt { 37 } } { 4 } , \frac { - 5 + \sqrt { 37 } } { 4 } \right\}$ 
D)  $\left\{ \frac { - 5 - \sqrt { 13 } } { 4 } , \frac { - 5 + \sqrt { 13 } } { 4 } \right\}$

Question 13

Solve.
-The base of a triangle is 8 more than twice its height. If the area of the triangle is 70 square centimeters, find its base and height.

Accepted Answer

A)  height: $4 + \sqrt { 74 } \mathrm {~cm}$
base: $- 2 + \sqrt { 74 } \mathrm {~cm}$ 
B)  height: $- 2 + \sqrt { 74 } \mathrm {~cm}$
base: $4 + \sqrt { 74 } \mathrm {~cm}$ 
C)  height: $- 2 + \sqrt { 74 } \mathrm {~cm}$
base: $4 + 2 \sqrt { 74 } \mathrm {~cm}$ 
D)  height: $4 + 2 \sqrt { 74 } \mathrm {~cm}$
base: $- 2 + \sqrt { 74 } \mathrm {~cm}$ 
A)  height: $4 + \sqrt { 74 } \mathrm {~cm}$
base: $- 2 + \sqrt { 74 } \mathrm {~cm}$ 
B)  height: $- 2 + \sqrt { 74 } \mathrm {~cm}$
base: $4 + \sqrt { 74 } \mathrm {~cm}$ 
C)  height: $- 2 + \sqrt { 74 } \mathrm {~cm}$
base: $4 + 2 \sqrt { 74 } \mathrm {~cm}$ 
D)  height: $4 + 2 \sqrt { 74 } \mathrm {~cm}$
base: $- 2 + \sqrt { 74 } \mathrm {~cm}$

Question 14

Use the square root property to solve the equation.
$( 2 x + 2 ) ^ { 2 } = 16$

Accepted Answer

A)  $\{ 0,1 \}$ 
B)  $\{ 1 , - 3 \}$ 
C)  $\{ 1,3 \}$ 
D)  $\{ 9 , - 9 \}$ 
A)  $\{ 0,1 \}$ 
B)  $\{ 1 , - 3 \}$ 
C)  $\{ 1,3 \}$ 
D)  $\{ 9 , - 9 \}$

Question 15

Solve.
-A rain gutter is made from sheets of aluminum that are 26 inches wide. The edges are turned up to form right angles. Determine the depth of the gutter that will allow a cross-sectional area of 53 square inches. There are
Two solutions to this problem. Round to the nearest tenth of an inch.

Accepted Answer

A)  2.2 in. and 23.8 in. 
B)  3.0 in. and 12.6 in. 
C)  2.5 in. and 10.5 in. 
D)  1.8 in. and 19.0 in. 
A)  2.2 in. and 23.8 in. 
B)  3.0 in. and 12.6 in. 
C)  2.5 in. and 10.5 in. 
D)  1.8 in. and 19.0 in.

Question 16

Solve.
-$$( 2 x - 4 ) ^ { 2 } - 4 ( 2 x - 4 ) - 21 = 0$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } , \frac { 11 } { 2 } \right\}$ 
B)  $\left\{ \frac { 7 } { 2 } , - \frac { 3 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 2 } , - \frac { 11 } { 2 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 4 } , \frac { 3 } { 2 } \right\}$ 
A)  $\left\{ \frac { 1 } { 2 } , \frac { 11 } { 2 } \right\}$ 
B)  $\left\{ \frac { 7 } { 2 } , - \frac { 3 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 2 } , - \frac { 11 } { 2 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 4 } , \frac { 3 } { 2 } \right\}$

Question 17

Graph the function. Label the vertex.
-$f(x)=-2(x-1)^{2}-6$

Accepted Answer

A)  Vertex: $( - 6,1 )$
  
B)  Vertex: $( 1 , - 6 )$
  
C)  Vertex: $( - 1 , - 6 )$
  
D)  Vertex: $( 6 , - 1 )$
  
A)  Vertex: $( - 6,1 )$
  
B)  Vertex: $( 1 , - 6 )$
  
C)  Vertex: $( - 1 , - 6 )$
  
D)  Vertex: $( 6 , - 1 )$

Question 18

Use the quadratic formula to solve the equation.
-$$\frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 4 } x - \frac { 1 } { 2 } = 0$$

Accepted Answer

A)  $\left\{ \frac { - 1 - i \sqrt { 15 } } { 4 } , \frac { - 1 + i \sqrt { 15 } } { 4 } \right\}$ 
B)  $\{ - 1 \}$ 
C)  $\left\{ - \frac { 5 } { 4 } , \frac { 3 } { 4 } \right\}$ 
D)  $\left\{ \frac { - 1 - \sqrt { 17 } } { 4 } , \frac { - 1 + \sqrt { 17 } } { 4 } \right\}$ 
A)  $\left\{ \frac { - 1 - i \sqrt { 15 } } { 4 } , \frac { - 1 + i \sqrt { 15 } } { 4 } \right\}$ 
B)  $\{ - 1 \}$ 
C)  $\left\{ - \frac { 5 } { 4 } , \frac { 3 } { 4 } \right\}$ 
D)  $\left\{ \frac { - 1 - \sqrt { 17 } } { 4 } , \frac { - 1 + \sqrt { 17 } } { 4 } \right\}$

Question 19

Solve the inequality. Write the solution set in interval notation.
-$$\frac { ( x - 2 ) ( x + 2 ) } { x } \leq 0$$

Accepted Answer

A)  $[ - 2,0 ) \cup [ 2 , \infty )$ 
B)  $( - \infty , - 2 ] \cup [ 2 , \infty )$ 
C)  $[ - 2,0 ) \cup ( 0,2 ]$ 
D)  $( - \infty , - 2 ] \cup ( 0,2 ]$ 
A)  $[ - 2,0 ) \cup [ 2 , \infty )$ 
B)  $( - \infty , - 2 ] \cup [ 2 , \infty )$ 
C)  $[ - 2,0 ) \cup ( 0,2 ]$ 
D)  $( - \infty , - 2 ] \cup ( 0,2 ]$

Question 20

Match the function with its graph.
-$f ( x ) = - x ^ { 2 } + 2 x$

Accepted Answer

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

Solve by completing the square. - $x ^ { 2 } + 16 x = - 43$

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - $x ^ { 2 } + 14 x$

Graph the function. Find and label the vertex, y-intercept, and x-intercepts (if any). - $F(x)=2 x^{2}-4 x+3$ $Graph the function. Find and label the vertex, y-intercept, and x-intercepts (if any). - F(x)=2 x^{2}-4 x+3$

Use the quadratic formula to solve the equation. - $5 x ^ { 2 } + 7 x + 9 = 0$

Match the function with its graph. - $f ( x ) = x ^ { 2 } - 2 x - 8$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f ( x ) = - \frac { 1 } { 4 } x ^ { 2 }$ $Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f ( x ) = - \frac { 1 } { 4 } x ^ { 2 }$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f ( x ) = x ^ { 2 } - 5$ $Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f ( x ) = x ^ { 2 } - 5$

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

Solve. -The cost in millions of dollars for a company to manufacture $x$ thousand automobiles is given by the function $C ( x ) = 5 x ^ { 2 } - 30 x + 81$ . Find the number of automobiles that must be produced to minimize the cost.

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - $x ^ { 2 } + \frac { 1 } { 6 } x$

Solve. -The area of a square porch is 121 square feet. Find the dimensions of the porch.

Use the quadratic formula to solve the equation. - $4 x ^ { 2 } + 10 x = - 3$

Solve. -The base of a triangle is 8 more than twice its height. If the area of the triangle is 70 square centimeters, find its base and height.

Use the square root property to solve the equation. $( 2 x + 2 ) ^ { 2 } = 16$

Solve. -A rain gutter is made from sheets of aluminum that are 26 inches wide. The edges are turned up to form right angles. Determine the depth of the gutter that will allow a cross-sectional area of 53 square inches. There are Two solutions to this problem. Round to the nearest tenth of an inch.

Solve. - $( 2 x - 4 ) ^ { 2 } - 4 ( 2 x - 4 ) - 21 = 0$

Graph the function. Label the vertex. - $f(x)=-2(x-1)^{2}-6$ $Graph the function. Label the vertex. - f(x)=-2(x-1)^{2}-6$

Use the quadratic formula to solve the equation. - $\frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 4 } x - \frac { 1 } { 2 } = 0$

Solve the inequality. Write the solution set in interval notation. - $\frac { ( x - 2 ) ( x + 2 ) } { x } \leq 0$

Match the function with its graph. - $f ( x ) = - x ^ { 2 } + 2 x$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

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Exam 8: Quadratic Equations and Functions

Solve by completing the square. - x2+16x=−43x ^ { 2 } + 16 x = - 43x2+16x=−43

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - x2+14xx ^ { 2 } + 14 xx2+14x

Graph the function. Find and label the vertex, y-intercept, and x-intercepts (if any). - F(x)=2x2−4x+3F(x)=2 x^{2}-4 x+3F(x)=2x2−4x+3

Use the quadratic formula to solve the equation. - 5x2+7x+9=05 x ^ { 2 } + 7 x + 9 = 05x2+7x+9=0

Match the function with its graph. - f(x)=x2−2x−8f ( x ) = x ^ { 2 } - 2 x - 8f(x)=x2−2x−8

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=−14x2f ( x ) = - \frac { 1 } { 4 } x ^ { 2 }f(x)=−41​x2

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=x2−5f ( x ) = x ^ { 2 } - 5f(x)=x2−5

Solve. - x3+x+2x2+2=0x ^ { 3 } + x + 2 x ^ { 2 } + 2 = 0x3+x+2x2+2=0

Solve. -The cost in millions of dollars for a company to manufacture xxx thousand automobiles is given by the function C(x)=5x2−30x+81C ( x ) = 5 x ^ { 2 } - 30 x + 81C(x)=5x2−30x+81 . Find the number of automobiles that must be produced to minimize the cost.

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - x2+16xx ^ { 2 } + \frac { 1 } { 6 } xx2+61​x