Question 1

Solve the inequality. Write the solution set in interval notation.
-$$( x + 6 ) ( x - 1 ) ( x - 2 ) > 0$$

Accepted Answer

A)  $( - \infty , - 6 ) \cup ( 1,2 )$ 
B)  $( - 6,1 ) \cup ( 2 , \infty )$ 
C)  $( 2 , \infty )$ 
D)  $( - \infty , 1 )$ 
A)  $( - \infty , - 6 ) \cup ( 1,2 )$ 
B)  $( - 6,1 ) \cup ( 2 , \infty )$ 
C)  $( 2 , \infty )$ 
D)  $( - \infty , 1 )$

Question 2

Use the square root property to solve the equation.
$( 3 x + 4 ) ^ { 2 } + 5 = 0$

Accepted Answer

A)  $\left\{ \frac { - 4 + i \sqrt { 5 } } { 3 } , \frac { - 4 - i \sqrt { 5 } } { 3 } \right\}$ 
B)  $\left\{ \frac { \sqrt { 5 } + 4 } { 3 } , \frac { \sqrt { 5 } - 4 } { 3 } \right\}$ 
C)  $\left\{ \frac { - 4 + \sqrt { 5 } } { 3 } , \frac { - 4 - \sqrt { 5 } } { 3 } \right\}$ 
D)  $\left\{ - \frac { 9 } { 3 } , \frac { 1 } { 3 } \right\}$ 
A)  $\left\{ \frac { - 4 + i \sqrt { 5 } } { 3 } , \frac { - 4 - i \sqrt { 5 } } { 3 } \right\}$ 
B)  $\left\{ \frac { \sqrt { 5 } + 4 } { 3 } , \frac { \sqrt { 5 } - 4 } { 3 } \right\}$ 
C)  $\left\{ \frac { - 4 + \sqrt { 5 } } { 3 } , \frac { - 4 - \sqrt { 5 } } { 3 } \right\}$ 
D)  $\left\{ - \frac { 9 } { 3 } , \frac { 1 } { 3 } \right\}$

Question 3

Solve the inequality. Write the solution set in interval notation.
-$$4 x ^ { 2 } - 5 x \geq 9$$

Accepted Answer

A)  $\left[ - 1 , \frac { 9 } { 4 } \right]$ 
B)  $\left( - 1 , \frac { 9 } { 4 } \right)$ 
C)  $( - \infty , - 1 ] \cup \left[ \frac { 9 } { 4 } , \infty \right)$ 
D)  $( - \infty , - 1 ) \cup \left( \frac { 9 } { 4 } , \infty \right)$ 
A)  $\left[ - 1 , \frac { 9 } { 4 } \right]$ 
B)  $\left( - 1 , \frac { 9 } { 4 } \right)$ 
C)  $( - \infty , - 1 ] \cup \left[ \frac { 9 } { 4 } , \infty \right)$ 
D)  $( - \infty , - 1 ) \cup \left( \frac { 9 } { 4 } , \infty \right)$

Question 4

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

-If $\mathrm { a } ^ { 2 } = \mathrm { b }$, then $\mathrm { a } =ــــــــــ$

Accepted Answer

A)  $\frac { - b } { 2 a }$ 
B)  $( 0 , \mathrm { k } )$ 
C)  $( h , 0 )$ 
D)  $\pm \sqrt { b }$ 
A)  $\frac { - b } { 2 a }$ 
B)  $( 0 , \mathrm { k } )$ 
C)  $( h , 0 )$ 
D)  $\pm \sqrt { b }$

Question 5

Use the quadratic formula to solve the equation.
-$$( x + 3 ) ( x - 1 ) = 0$$

Accepted Answer

A)  $\{ 1 - 1,1 + 1 \}$ 
B)  $[ - 1 - \sqrt { 7 } , - 1 + \sqrt { 7 } \}$ 
C)  $\{ - 1 - 1 , - 1 + 1 \}$ 
D)  $\{ 1 - \sqrt { 7 } , 1 + \sqrt { 7 } \}$ 
A)  $\{ 1 - 1,1 + 1 \}$ 
B)  $[ - 1 - \sqrt { 7 } , - 1 + \sqrt { 7 } \}$ 
C)  $\{ - 1 - 1 , - 1 + 1 \}$ 
D)  $\{ 1 - \sqrt { 7 } , 1 + \sqrt { 7 } \}$

Question 6

Use the quadratic formula to solve the equation.
-$$x ( 5 x + 9 ) = 4$$

Accepted Answer

A)  $\left\{ \frac { - 9 - 1 } { 10 } , \frac { - 9 + 1 } { 10 } \right\}$ 
B)  $\left\{ \frac { 9 - 1 } { 10 } , \frac { 9 + 1 } { 10 } \right\}$ 
C)  $\left\{ \frac { - 9 - \sqrt { 161 } } { 10 } , \frac { - 9 + \sqrt { 161 } } { 10 } \right\}$ 
D)  $\left\{ \frac { 9 - \sqrt { 161 } } { 10 } , \frac { 9 + \sqrt { 161 } } { 10 } \right\}$ 
A)  $\left\{ \frac { - 9 - 1 } { 10 } , \frac { - 9 + 1 } { 10 } \right\}$ 
B)  $\left\{ \frac { 9 - 1 } { 10 } , \frac { 9 + 1 } { 10 } \right\}$ 
C)  $\left\{ \frac { - 9 - \sqrt { 161 } } { 10 } , \frac { - 9 + \sqrt { 161 } } { 10 } \right\}$ 
D)  $\left\{ \frac { 9 - \sqrt { 161 } } { 10 } , \frac { 9 + \sqrt { 161 } } { 10 } \right\}$

Question 7

Use the square root property to solve the equation.
$x ^ { 2 } - 19 = 0$

Accepted Answer

A)  $\{ - \sqrt { 19 } , \sqrt { 19 } \}$ 
B)  $\left\{ \frac { 19 } { 2 } \right\}$ 
C)  $\{ \sqrt { 19 } \}$ 
D)  $\{ 361 \}$ 
A)  $\{ - \sqrt { 19 } , \sqrt { 19 } \}$ 
B)  $\left\{ \frac { 19 } { 2 } \right\}$ 
C)  $\{ \sqrt { 19 } \}$ 
D)  $\{ 361 \}$

Question 8

Solve.
-$x ^ { 4 } - 4 x ^ { 2 } - 45 = 0$

Accepted Answer

A)  $\{ 3 , i \sqrt { 5 } \}$ 
B)  $\{ - \sqrt { 5 } , \sqrt { 5 } , - 3 i , 3 i \}$ 
C)  $\{ - 9,5 \}$ 
D)  $\{ - 3,3 , - \mathrm { i } \sqrt { 5 } , \mathrm { i } \sqrt { 5 } \}$ 
A)  $\{ 3 , i \sqrt { 5 } \}$ 
B)  $\{ - \sqrt { 5 } , \sqrt { 5 } , - 3 i , 3 i \}$ 
C)  $\{ - 9,5 \}$ 
D)  $\{ - 3,3 , - \mathrm { i } \sqrt { 5 } , \mathrm { i } \sqrt { 5 } \}$

Question 9

Use the square root property to solve the equation.
$( 4 x + 3 ) ^ { 2 } = 6$

Accepted Answer

A)  $\left\{ - \frac { 9 } { 4 } , \frac { 3 } { 4 } \right\}$ 
B)  $\left\{ \frac { - 3 - \sqrt { 6 } } { 4 } , \frac { - 3 + \sqrt { 6 } } { 4 } \right\}$ 
C)  $\left\{ \frac { \sqrt { 6 } - 3 } { 4 } , \frac { \sqrt { 6 } + 3 } { 4 } \right\}$ 
D)  $\left\{ \frac { 3 - \sqrt { 6 } } { 4 } , \frac { 3 + \sqrt { 6 } } { 4 } \right\}$ 
A)  $\left\{ - \frac { 9 } { 4 } , \frac { 3 } { 4 } \right\}$ 
B)  $\left\{ \frac { - 3 - \sqrt { 6 } } { 4 } , \frac { - 3 + \sqrt { 6 } } { 4 } \right\}$ 
C)  $\left\{ \frac { \sqrt { 6 } - 3 } { 4 } , \frac { \sqrt { 6 } + 3 } { 4 } \right\}$ 
D)  $\left\{ \frac { 3 - \sqrt { 6 } } { 4 } , \frac { 3 + \sqrt { 6 } } { 4 } \right\}$

Question 10

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

Accepted Answer

A)  Vertex: $( - 4,1 )$; axis: $x = - 4$
  
B)  Vertex: $( 1,4 )$; axis: $x = 1$
  
C)  Vertex: $( - 1,4 )$; axis: $x = - 1$
  
D)  Vertex: $( 4 , - 1 )$; axis: $x = 4$
  
A)  Vertex: $( - 4,1 )$; axis: $x = - 4$
  
B)  Vertex: $( 1,4 )$; axis: $x = 1$
  
C)  Vertex: $( - 1,4 )$; axis: $x = - 1$
  
D)  Vertex: $( 4 , - 1 )$; axis: $x = 4$

Question 11

Use the discriminant to determine the number and type of solutions of the equation.
-$$x ^ { 2 } - 12 x + 36 = 0$$

Accepted Answer

A)  Two real solutions 
B)  Two complex but not real solutions 
C)  One real solution 
A)  Two real solutions 
B)  Two complex but not real solutions 
C)  One real solution

Question 12

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
-$$x ^ { 2 } - 13 x$$

Accepted Answer

A)  $x ^ { 2 } - 13 x + \frac { 13 } { 2 } = \left( x - \frac { 13 } { 2 } \right) ^ { 2 }$ 
B)  $x ^ { 2 } - 13 x - \frac { 169 } { 4 } = \left( x - \frac { 13 } { 2 } \right) ^ { 2 }$ 
C)  $x ^ { 2 } - 13 x + 169 = ( x - 13 ) ^ { 2 }$ 
D)  $x ^ { 2 } - 13 x + \frac { 169 } { 4 } = \left( x - \frac { 13 } { 2 } \right) ^ { 2 }$ 
A)  $x ^ { 2 } - 13 x + \frac { 13 } { 2 } = \left( x - \frac { 13 } { 2 } \right) ^ { 2 }$ 
B)  $x ^ { 2 } - 13 x - \frac { 169 } { 4 } = \left( x - \frac { 13 } { 2 } \right) ^ { 2 }$ 
C)  $x ^ { 2 } - 13 x + 169 = ( x - 13 ) ^ { 2 }$ 
D)  $x ^ { 2 } - 13 x + \frac { 169 } { 4 } = \left( x - \frac { 13 } { 2 } \right) ^ { 2 }$

Question 13

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function.
-$f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + 4 x + \frac { 15 } { 2 }$

Accepted Answer

A)  Vertex: $\left( - 4 , - \frac { 1 } { 2 } \right)$
$x$-intercepts: $( - 5,0 )$ and $( - 3,0 )$;
$y$-intercept: $\left( 0 , \frac { 15 } { 2 } \right)$
  
B)  Vertex: $\left( 4 , \frac { 1 } { 2 } \right)$;
$x$-intercepts: $( 5,0 )$ and $( 3,0 )$;
$y$-intercept: $\left( 0 , - \frac { 15 } { 2 } \right)$
  
C)  Vertex: $\left( 4 , - \frac { 1 } { 2 } \right)$
$x$-intercepts: $( 5,0 )$ and $( 3,0 )$;
$y$-intercept $\left( 0 , \frac { 15 } { 2 } \right)$
  
D)  Vertex: $\left( - 4 , \frac { 1 } { 2 } \right)$
$x$-intercepts: $( - 5,0 )$ and $( - 3,0 )$;
$y \text {-intercept: }\left(0,-\frac{15}{2}\right)$
  
A)  Vertex: $\left( - 4 , - \frac { 1 } { 2 } \right)$
$x$-intercepts: $( - 5,0 )$ and $( - 3,0 )$;
$y$-intercept: $\left( 0 , \frac { 15 } { 2 } \right)$
  
B)  Vertex: $\left( 4 , \frac { 1 } { 2 } \right)$;
$x$-intercepts: $( 5,0 )$ and $( 3,0 )$;
$y$-intercept: $\left( 0 , - \frac { 15 } { 2 } \right)$
  
C)  Vertex: $\left( 4 , - \frac { 1 } { 2 } \right)$
$x$-intercepts: $( 5,0 )$ and $( 3,0 )$;
$y$-intercept $\left( 0 , \frac { 15 } { 2 } \right)$
  
D)  Vertex: $\left( - 4 , \frac { 1 } { 2 } \right)$
$x$-intercepts: $( - 5,0 )$ and $( - 3,0 )$;
$y \text {-intercept: }\left(0,-\frac{15}{2}\right)$

Question 14

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 3 } + 2 x ^ { 2 } - 11 x + 20 \leq 0$$

Accepted Answer

A)  $[ - 5 , \infty )$ 
B)  $( - \infty , - 5 ] \cup [ 4 , \infty )$ 
C)  $( - \infty , - 5 ]$ 
D)  $( - \infty , - 5 ] \cup [ - 3,4 ]$ 
A)  $[ - 5 , \infty )$ 
B)  $( - \infty , - 5 ] \cup [ 4 , \infty )$ 
C)  $( - \infty , - 5 ]$ 
D)  $( - \infty , - 5 ] \cup [ - 3,4 ]$

Question 15

Use the quadratic formula to solve the equation.
-$$2 y - \frac { 3 } { 5 } = \frac { 3 } { 5 } y ^ { 2 }$$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\left\{ \frac { 5 - i \sqrt { 34 } } { 3 } , \frac { 5 + i \sqrt { 34 } } { 3 } \right\}$ 
C)  $\left\{ \frac { 1 } { 3 } , 3 \right\}$ 
D)  $\left\{ \frac { 10 - \sqrt { 76 } } { 6 } , \frac { 10 + \sqrt { 76 } } { 6 } \right\}$ 
A)  $\{ 3 \}$ 
B)  $\left\{ \frac { 5 - i \sqrt { 34 } } { 3 } , \frac { 5 + i \sqrt { 34 } } { 3 } \right\}$ 
C)  $\left\{ \frac { 1 } { 3 } , 3 \right\}$ 
D)  $\left\{ \frac { 10 - \sqrt { 76 } } { 6 } , \frac { 10 + \sqrt { 76 } } { 6 } \right\}$

Question 16

Solve.
-The owner of a video store has determined that the cost function, in dollars, of operating the store, is approximately given by $C ( x ) = 2 x ^ { 2 } - 24 x + 600$, where $x$ is the number of videos rented daily. Find the lowest cost to the nearest dollar.

Accepted Answer

A)  $\$ 672$ 
B)  $\$ 456$ 
C)  $\$ 312$ 
D)  $\$ 528$ 
A)  $\$ 672$ 
B)  $\$ 456$ 
C)  $\$ 312$ 
D)  $\$ 528$

Question 17

Match the function with its graph.
-$f ( x ) = - x ^ { 2 } + 9$

Accepted Answer

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

Question 18

Use the discriminant to determine the number and type of solutions of the equation.
-$$x ^ { 2 } - 4 x - 1 = 0$$

Accepted Answer

A)  One real solution 
B)  Two complex but not real solutions 
C)  Two real solutions 
A)  One real solution 
B)  Two complex but not real solutions 
C)  Two real solutions

Question 19

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function.
-$f ( x ) = x ^ { 2 } + 3 x + 2$

Accepted Answer

A)  Vertex: $\left( \frac { 3 } { 2 } , - \frac { 1 } { 4 } \right)$;
$x$-intercepts: $( 1,0 )$ and $( 2,0 )$;
y-intercept: $( 0,2 )$
  
B)  Vertex: $\left( - \frac { 3 } { 2 } , - \frac { 1 } { 4 } \right)$;
$x$-intercepts: $( - 1,0 )$ and $( - 2,0 )$;
y-intercept: $( 0,2 )$
  
C)  Vertex: $\left( \frac { 3 } { 2 } , - \frac { 1 } { 4 } \right)$
$x$-intercepts: $( - 1,0 )$ and $( - 2,0 )$;
y-intercept: $( 0,2 )$
  
D)  Vertex: $\left( - \frac { 3 } { 2 } , - \frac { 1 } { 4 } \right)$;
$x$-intercepts: $( 1,0 )$ and $( 2,0 )$;
y-intercept: $( 0,2 )$
  
A)  Vertex: $\left( \frac { 3 } { 2 } , - \frac { 1 } { 4 } \right)$;
$x$-intercepts: $( 1,0 )$ and $( 2,0 )$;
y-intercept: $( 0,2 )$
  
B)  Vertex: $\left( - \frac { 3 } { 2 } , - \frac { 1 } { 4 } \right)$;
$x$-intercepts: $( - 1,0 )$ and $( - 2,0 )$;
y-intercept: $( 0,2 )$
  
C)  Vertex: $\left( \frac { 3 } { 2 } , - \frac { 1 } { 4 } \right)$
$x$-intercepts: $( - 1,0 )$ and $( - 2,0 )$;
y-intercept: $( 0,2 )$
  
D)  Vertex: $\left( - \frac { 3 } { 2 } , - \frac { 1 } { 4 } \right)$;
$x$-intercepts: $( 1,0 )$ and $( 2,0 )$;
y-intercept: $( 0,2 )$

Question 20

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

-The formula $x = \frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ is called theـــــــــــــــــــ

Accepted Answer

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

Solve the inequality. Write the solution set in interval notation. - $( x + 6 ) ( x - 1 ) ( x - 2 ) > 0$

Use the square root property to solve the equation. $( 3 x + 4 ) ^ { 2 } + 5 = 0$

Solve the inequality. Write the solution set in interval notation. - $4 x ^ { 2 } - 5 x \geq 9$

Use the quadratic formula to solve the equation. - $( x + 3 ) ( x - 1 ) = 0$

Use the quadratic formula to solve the equation. - $x ( 5 x + 9 ) = 4$

Use the square root property to solve the equation. $x ^ { 2 } - 19 = 0$

Solve. - $x ^ { 4 } - 4 x ^ { 2 } - 45 = 0$

Use the square root property to solve the equation. $( 4 x + 3 ) ^ { 2 } = 6$

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

Use the discriminant to determine the number and type of solutions of the equation. - $x ^ { 2 } - 12 x + 36 = 0$

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - $x ^ { 2 } - 13 x$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 3 } + 2 x ^ { 2 } - 11 x + 20 \leq 0$

Use the quadratic formula to solve the equation. - $2 y - \frac { 3 } { 5 } = \frac { 3 } { 5 } y ^ { 2 }$

Solve. -The owner of a video store has determined that the cost function, in dollars, of operating the store, is approximately given by $C ( x ) = 2 x ^ { 2 } - 24 x + 600$ , where $x$ is the number of videos rented daily. Find the lowest cost to the nearest dollar.

Match the function with its graph. - $f ( x ) = - x ^ { 2 } + 9$

Use the discriminant to determine the number and type of solutions of the equation. - $x ^ { 2 } - 4 x - 1 = 0$

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - $f ( x ) = x ^ { 2 } + 3 x + 2$ $Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - f ( x ) = x ^ { 2 } + 3 x + 2$

Real Numbers and Algebraic Expressions

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Exam 8: Quadratic Equations and Functions

Solve the inequality. Write the solution set in interval notation. - (x+6)(x−1)(x−2)>0( x + 6 ) ( x - 1 ) ( x - 2 ) > 0(x+6)(x−1)(x−2)>0

Use the square root property to solve the equation. (3x+4)2+5=0( 3 x + 4 ) ^ { 2 } + 5 = 0(3x+4)2+5=0

Solve the inequality. Write the solution set in interval notation. - 4x2−5x≥94 x ^ { 2 } - 5 x \geq 94x2−5x≥9

Fill in the blank with one of the words or phrases listed below. -If a2=b\mathrm { a } ^ { 2 } = \mathrm { b }a2=b , then a=ــــــــــ\mathrm { a } =ــــــــــa=ــــــــــ

Use the quadratic formula to solve the equation. - (x+3)(x−1)=0( x + 3 ) ( x - 1 ) = 0(x+3)(x−1)=0

Use the quadratic formula to solve the equation. - x(5x+9)=4x ( 5 x + 9 ) = 4x(5x+9)=4

Use the square root property to solve the equation. x2−19=0x ^ { 2 } - 19 = 0x2−19=0

Solve. - x4−4x2−45=0x ^ { 4 } - 4 x ^ { 2 } - 45 = 0x4−4x2−45=0

Use the square root property to solve the equation. (4x+3)2=6( 4 x + 3 ) ^ { 2 } = 6(4x+3)2=6

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

Use the discriminant to determine the number and type of solutions of the equation. - x2−12x+36=0x ^ { 2 } - 12 x + 36 = 0x2−12x+36=0

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - x2−13xx ^ { 2 } - 13 xx2−13x

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - f(x)=12x2+4x+152f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + 4 x + \frac { 15 } { 2 }f(x)=21​x2+4x+215​

Solve the inequality. Write the solution set in interval notation. - x3+2x2−11x+20≤0x ^ { 3 } + 2 x ^ { 2 } - 11 x + 20 \leq 0x3+2x2−11x+20≤0

Use the quadratic formula to solve the equation. - 2y−35=35y22 y - \frac { 3 } { 5 } = \frac { 3 } { 5 } y ^ { 2 }2y−53​=53​y2

Match the function with its graph. - f(x)=−x2+9f ( x ) = - x ^ { 2 } + 9f(x)=−x2+9

Use the discriminant to determine the number and type of solutions of the equation. - x2−4x−1=0x ^ { 2 } - 4 x - 1 = 0x2−4x−1=0

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - f(x)=x2+3x+2f ( x ) = x ^ { 2 } + 3 x + 2f(x)=x2+3x+2

Fill in the blank with one of the words or phrases listed below. -The formula x=−b±b2−4ac2ax = \frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }x=2a−b±b2−4ac​​ is called theـــــــــــــــــــ