Question 1

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$( x + 3 ) ( x + 1 ) ( x - 3 ) < 0$

Accepted Answer

A)  $( 3 , \infty )$
  
B)  $( - \infty , - 1 )$
  
C)  $( - 3 , - 1 ) \cup ( 3 , \infty )$
  
D)  $( - \infty , - 3 ) \cup ( - 1,3 )$
  
A)  $( 3 , \infty )$
  
B)  $( - \infty , - 1 )$
  
C)  $( - 3 , - 1 ) \cup ( 3 , \infty )$
  
D)  $( - \infty , - 3 ) \cup ( - 1,3 )$

Question 2

Find the vertex of the graph of the quadratic function.
-$f ( x ) = - x ^ { 2 } - 12 x + 1$

Accepted Answer

A)  $( - 6,37 )$ 
B)  $( - 12,1 )$ 
C)  $( 6 , - 107 )$ 
D)  $( 6 , - 35 )$ 
A)  $( - 6,37 )$ 
B)  $( - 12,1 )$ 
C)  $( 6 , - 107 )$ 
D)  $( 6 , - 35 )$

Question 3

Solve.
-$x - 8 \sqrt { x } + 12 = 0$

Accepted Answer

A)  36,4 
B)  $- \sqrt { 6 } , \sqrt { 6 } , - \sqrt { 2 } , \sqrt { 2 }$ 
C)  6,2 
D)  $- 6,6 , - 2,2$ 
A)  36,4 
B)  $- \sqrt { 6 } , \sqrt { 6 } , - \sqrt { 2 } , \sqrt { 2 }$ 
C)  6,2 
D)  $- 6,6 , - 2,2$

Question 4

Solve the inequality. Write the solution set in interval notation.
-$\frac { 4 x - 24 } { x ^ { 2 } - 1 } \geq 0$

Accepted Answer

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

Question 5

Solve.
-$2 x ^ { 2 / 3 } - 7 x ^ { 1 / 3 } - 15 = 0$

Accepted Answer

A)  $125 , \frac { 27 } { 8 }$ 
B)  $- \frac { 27 } { 8 }$ 
C)  $125 , - \frac { 27 } { 8 }$ 
D)  125 
A)  $125 , \frac { 27 } { 8 }$ 
B)  $- \frac { 27 } { 8 }$ 
C)  $125 , - \frac { 27 } { 8 }$ 
D)  125

Question 6

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

Accepted Answer

A)  vertex $( 0,2 )$; axis $x = 0$
  
B)  vertex $( 0 , - 2 )$; axis $x = 0$
  
C)  vertex $( - 2,0 )$; axis $x = - 2$
  
D)  vertex $( 2,0 )$; axis $x = 2$
  
A)  vertex $( 0,2 )$; axis $x = 0$
  
B)  vertex $( 0 , - 2 )$; axis $x = 0$
  
C)  vertex $( - 2,0 )$; axis $x = - 2$
  
D)  vertex $( 2,0 )$; axis $x = 2$

Question 7

Solve.
-$x ^ { 2 / 3 } - 2 x ^ { 1 / 3 } - 8 = 0$

Accepted Answer

A)  $- 4,2$ 
B)  $- 2,4$ 
C)  $- 64,8$ 
D)  $- 8,64$ 
A)  $- 4,2$ 
B)  $- 2,4$ 
C)  $- 64,8$ 
D)  $- 8,64$

Question 8

Solve.
-$( 3 x + 2 ) ^ { 2 } - 11 ( 3 x + 2 ) = - 28$

Accepted Answer

A)  $\frac { 9 } { 3 } , - \frac { 6 } { 3 }$ 
B)  $- \frac { 5 } { 3 } , - \frac { 2 } { 3 }$ 
C)  $- \frac { 9 } { 2 } , \frac { 6 } { 3 }$ 
D)  $\frac { 5 } { 3 } , \frac { 2 } { 3 }$ 
A)  $\frac { 9 } { 3 } , - \frac { 6 } { 3 }$ 
B)  $- \frac { 5 } { 3 } , - \frac { 2 } { 3 }$ 
C)  $- \frac { 9 } { 2 } , \frac { 6 } { 3 }$ 
D)  $\frac { 5 } { 3 } , \frac { 2 } { 3 }$

Question 9

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l l } 
\text { quadratic formula } & \text { quadratic } & \text { discriminant } & \pm \sqrt { b } \
\text { completing the square } & \text { quadratic inequality } & ( h , k ) & ( 0 , k ) \
( h , 0 ) & \frac { - b } { 2 a } & &
\end{array}$$
-The graph of $f ( x ) = a x ^ { 2 } + b x + c$ where $a$ is not 0 is a parabola whose vertex has $x$-value of________

Accepted Answer

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

Question 10

Solve.
-$\frac { 12 } { x ^ { 2 } } = \frac { 6 } { x + 8 }$

Accepted Answer

A)  $- 1 - \sqrt { 17 } , - 1 + \sqrt { 17 }$ 
B)  $1 - \mathrm { i } \sqrt { 15 } , 1 + \mathrm { i } \sqrt { 15 }$ 
C)  $- 1 - \mathrm { i } \sqrt { 15 } , - 1 + \mathrm { i } \sqrt { 15 }$ 
D)  $1 - \sqrt { 17 } , 1 + \sqrt { 17 }$ 
A)  $- 1 - \sqrt { 17 } , - 1 + \sqrt { 17 }$ 
B)  $1 - \mathrm { i } \sqrt { 15 } , 1 + \mathrm { i } \sqrt { 15 }$ 
C)  $- 1 - \mathrm { i } \sqrt { 15 } , - 1 + \mathrm { i } \sqrt { 15 }$ 
D)  $1 - \sqrt { 17 } , 1 + \sqrt { 17 }$

Question 11

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$( 6 y + 5 ) ( 5 y - 9 ) > 0$

Accepted Answer

A)  $\left( - \infty , - \frac { 5 } { 6 } \right) \cup \left( \frac { 9 } { 5 } , \infty \right)$
  
B)  $\left( - \infty , - \frac { 5 } { 6 } \right] \cup \left[ \frac { 9 } { 5 } , \infty \right)$
  
C)  $\left[ - \frac { 5 } { 6 } , \frac { 9 } { 5 } \right]$
  
D)  $\left( - \frac { 5 } { 6 } , \frac { 9 } { 5 } \right)$
  
A)  $\left( - \infty , - \frac { 5 } { 6 } \right) \cup \left( \frac { 9 } { 5 } , \infty \right)$
  
B)  $\left( - \infty , - \frac { 5 } { 6 } \right] \cup \left[ \frac { 9 } { 5 } , \infty \right)$
  
C)  $\left[ - \frac { 5 } { 6 } , \frac { 9 } { 5 } \right]$
  
D)  $\left( - \frac { 5 } { 6 } , \frac { 9 } { 5 } \right)$

Question 12

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l l } 
\text { quadratic formula } & \text { quadratic } & \text { discriminant } & \pm \sqrt { b } \
\text { completing the square } & \text { quadratic inequality } & ( h , k ) & ( 0 , k ) \
( h , 0 ) & \frac { - b } { 2 a } & &
\end{array}$$
-A -------------is an inequality that can be written so that one side is a quadratic expression and the other side is 0.

Accepted Answer

A)  quadratic formula 
B)  quadratic inequality 
C)  discriminant 
D)  quadratic 
A)  quadratic formula 
B)  quadratic inequality 
C)  discriminant 
D)  quadratic

Question 13

Solve.
-Shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut the lawn with a push mower. If they can cut the lawn in 8 hours working together find how long to the
Nearest tenth of an hour it takes for William to cut the lawn alone.

Accepted Answer

A)  14.0 hr 
B)  13.9 hr 
C)  18.9 hr 
D)  19.0 hr 
A)  14.0 hr 
B)  13.9 hr 
C)  18.9 hr 
D)  19.0 hr

Question 14

Given the accompanying graph of y = f(x), sketch the graph of the following.
-$y = f ( x - 3 ) - 2$
 
$y = f ( x )$

Accepted Answer

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

Question 15

Match the function with its graph.
-$f ( x ) = x ^ { 2 } - 4$

Accepted Answer

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

Question 16

Use the square root property to solve the equation.
-$( x - 6 ) ^ { 2 } = - 9$

Accepted Answer

A)  $- 6 - 3 i , - 6 + 3 i$, 
B)  $- 9 , - 3$ 
C)  $6 - 3 i , 6 + 3 i$ 
D)  3,9 
A)  $- 6 - 3 i , - 6 + 3 i$, 
B)  $- 9 , - 3$ 
C)  $6 - 3 i , 6 + 3 i$ 
D)  3,9

Question 17

Use the quadratic formula to solve the equation.
-$5 x ^ { 2 } - 4 x - 9 = 0$

Accepted Answer

A)  $\frac { 5 } { 9 } , - 1$ 
B)  $\frac { 9 } { 5 } , - 1$ 
C)  $\frac { 5 } { 9 } , 0$ 
D)  $\frac { 5 } { 9 } , 1$ 
A)  $\frac { 5 } { 9 } , - 1$ 
B)  $\frac { 9 } { 5 } , - 1$ 
C)  $\frac { 5 } { 9 } , 0$ 
D)  $\frac { 5 } { 9 } , 1$

Question 18

Solve.
-$\frac { 1 } { x } + \frac { 1 } { x + 6 } = \frac { x + 7 } { x + 6 }$

Accepted Answer

A)  $- 6 , - 1$ 
B)  6,1 
C)  1 
D)  $- 6,1$ 
A)  $- 6 , - 1$ 
B)  6,1 
C)  1 
D)  $- 6,1$

Question 19

Solve.
-$x - \sqrt { 9 x } = 1$

Accepted Answer

A)  $\frac { 11 - 3 \sqrt { 13 } } { 2 } , \frac { 11 + 3 \sqrt { 13 } } { 2 }$ 
B)  $\frac { 11 + 5 \sqrt { 5 } } { 2 }$ 
C)  $\frac { 11 + 3 \sqrt { 13 } } { 2 }$ 
D)  $\frac { - 11 - 3 \sqrt { 13 } } { 2 } , \frac { - 11 + 3 \sqrt { 13 } } { 2 }$ 
A)  $\frac { 11 - 3 \sqrt { 13 } } { 2 } , \frac { 11 + 3 \sqrt { 13 } } { 2 }$ 
B)  $\frac { 11 + 5 \sqrt { 5 } } { 2 }$ 
C)  $\frac { 11 + 3 \sqrt { 13 } } { 2 }$ 
D)  $\frac { - 11 - 3 \sqrt { 13 } } { 2 } , \frac { - 11 + 3 \sqrt { 13 } } { 2 }$

Question 20

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

Accepted Answer

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

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $( x + 3 ) ( x + 1 ) ( x - 3 ) < 0$

Find the vertex of the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } - 12 x + 1$

Solve. - $x - 8 \sqrt { x } + 12 = 0$

Solve the inequality. Write the solution set in interval notation. - $\frac { 4 x - 24 } { x ^ { 2 } - 1 } \geq 0$

Solve. - $2 x ^ { 2 / 3 } - 7 x ^ { 1 / 3 } - 15 = 0$

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

Solve. - $x ^ { 2 / 3 } - 2 x ^ { 1 / 3 } - 8 = 0$

Solve. - $( 3 x + 2 ) ^ { 2 } - 11 ( 3 x + 2 ) = - 28$

Fill in the blank with one of the words or phrases listed below. quadratic formula quadratic discriminant \pm completing the square quadratic inequality (h,k) (0,k) (h,0) -The graph of $f ( x ) = a x ^ { 2 } + b x + c$ where $a$ is not 0 is a parabola whose vertex has $x$ -value of________

Solve. - $\frac { 12 } { x ^ { 2 } } = \frac { 6 } { x + 8 }$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $( 6 y + 5 ) ( 5 y - 9 ) > 0$

Fill in the blank with one of the words or phrases listed below. quadratic formula quadratic discriminant \pm completing the square quadratic inequality (h,k) (0,k) (h,0) -A -------------is an inequality that can be written so that one side is a quadratic expression and the other side is 0.

Solve. -Shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut the lawn with a push mower. If they can cut the lawn in 8 hours working together find how long to the Nearest tenth of an hour it takes for William to cut the lawn alone.

Given the accompanying graph of y = f(x), sketch the graph of the following. - $y = f ( x - 3 ) - 2$ $y = f ( x )$

Match the function with its graph. - $f ( x ) = x ^ { 2 } - 4$

Use the square root property to solve the equation. - $( x - 6 ) ^ { 2 } = - 9$

Use the quadratic formula to solve the equation. - $5 x ^ { 2 } - 4 x - 9 = 0$

Solve. - $\frac { 1 } { x } + \frac { 1 } { x + 6 } = \frac { x + 7 } { x + 6 }$

Solve. - $x - \sqrt { 9 x } = 1$

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

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 11: Quadratic Equations and Functions

Solve the inequality. Graph the solution set and write the solution set in interval notation. - (x+3)(x+1)(x−3)<0( x + 3 ) ( x + 1 ) ( x - 3 ) < 0(x+3)(x+1)(x−3)<0

Find the vertex of the graph of the quadratic function. - f(x)=−x2−12x+1f ( x ) = - x ^ { 2 } - 12 x + 1f(x)=−x2−12x+1

Solve. - x−8x+12=0x - 8 \sqrt { x } + 12 = 0x−8x​+12=0

Solve the inequality. Write the solution set in interval notation. - 4x−24x2−1≥0\frac { 4 x - 24 } { x ^ { 2 } - 1 } \geq 0x2−14x−24​≥0

Solve. - 2x2/3−7x1/3−15=02 x ^ { 2 / 3 } - 7 x ^ { 1 / 3 } - 15 = 02x2/3−7x1/3−15=0

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

Solve. - x2/3−2x1/3−8=0x ^ { 2 / 3 } - 2 x ^ { 1 / 3 } - 8 = 0x2/3−2x1/3−8=0

Solve. - (3x+2)2−11(3x+2)=−28( 3 x + 2 ) ^ { 2 } - 11 ( 3 x + 2 ) = - 28(3x+2)2−11(3x+2)=−28

Solve. - 12x2=6x+8\frac { 12 } { x ^ { 2 } } = \frac { 6 } { x + 8 }x212​=x+86​

Solve the inequality. Graph the solution set and write the solution set in interval notation. - (6y+5)(5y−9)>0( 6 y + 5 ) ( 5 y - 9 ) > 0(6y+5)(5y−9)>0

Fill in the blank with one of the words or phrases listed below. quadratic formula quadratic discriminant \pm completing the square quadratic inequality (h,k) (0,k) (h,0) -A -------------is an inequality that can be written so that one side is a quadratic expression and the other side is 0.

Solve. -Shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut the lawn with a push mower. If they can cut the lawn in 8 hours working together find how long to the Nearest tenth of an hour it takes for William to cut the lawn alone.

Given the accompanying graph of y = f(x), sketch the graph of the following. - y=f(x−3)−2y = f ( x - 3 ) - 2y=f(x−3)−2 y=f(x)y = f ( x )y=f(x)

Match the function with its graph. - f(x)=x2−4f ( x ) = x ^ { 2 } - 4f(x)=x2−4

Use the square root property to solve the equation. - (x−6)2=−9( x - 6 ) ^ { 2 } = - 9(x−6)2=−9

Use the quadratic formula to solve the equation. - 5x2−4x−9=05 x ^ { 2 } - 4 x - 9 = 05x2−4x−9=0

Solve. - 1x+1x+6=x+7x+6\frac { 1 } { x } + \frac { 1 } { x + 6 } = \frac { x + 7 } { x + 6 }x1​+x+61​=x+6x+7​

Solve. - x−9x=1x - \sqrt { 9 x } = 1x−9x​=1

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

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $( x + 3 ) ( x + 1 ) ( x - 3 ) < 0$

Find the vertex of the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } - 12 x + 1$

Solve. - $x - 8 \sqrt { x } + 12 = 0$

Solve the inequality. Write the solution set in interval notation. - $\frac { 4 x - 24 } { x ^ { 2 } - 1 } \geq 0$

Solve. - $2 x ^ { 2 / 3 } - 7 x ^ { 1 / 3 } - 15 = 0$

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

Solve. - $x ^ { 2 / 3 } - 2 x ^ { 1 / 3 } - 8 = 0$

Solve. - $( 3 x + 2 ) ^ { 2 } - 11 ( 3 x + 2 ) = - 28$

Solve. - $\frac { 12 } { x ^ { 2 } } = \frac { 6 } { x + 8 }$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $( 6 y + 5 ) ( 5 y - 9 ) > 0$

Given the accompanying graph of y = f(x), sketch the graph of the following. - $y = f ( x - 3 ) - 2$ $y = f ( x )$

Match the function with its graph. - $f ( x ) = x ^ { 2 } - 4$

Use the square root property to solve the equation. - $( x - 6 ) ^ { 2 } = - 9$

Use the quadratic formula to solve the equation. - $5 x ^ { 2 } - 4 x - 9 = 0$

Solve. - $\frac { 1 } { x } + \frac { 1 } { x + 6 } = \frac { x + 7 } { x + 6 }$

Solve. - $x - \sqrt { 9 x } = 1$

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