Question 1

Solve the inequality. Write the solution set in interval notation.
-$x ^ { 2 } - 6 x \geq - 8$

Accepted Answer

A)  $( - \infty , 2 ] \cup [ 4 , \infty )$ 
B)  $( - \infty , 2 ]$ 
C)  $[ 4 , \infty )$ 
D)  $[ 2,4 ]$ 
A)  $( - \infty , 2 ] \cup [ 4 , \infty )$ 
B)  $( - \infty , 2 ]$ 
C)  $[ 4 , \infty )$ 
D)  $[ 2,4 ]$

Question 2

Solve the equation by completing the square.
-$x ^ { 2 } + 12 x = - 26$

Accepted Answer

A)  $- 12 + \sqrt { 26 }$ 
B)  $6 + \sqrt { 10 }$ 
C)  $- 6 - \sqrt { 10 } , - 6 + \sqrt { 10 }$ 
D)  $6 - \sqrt { 26 } , 6 + \sqrt { 26 }$ 
A)  $- 12 + \sqrt { 26 }$ 
B)  $6 + \sqrt { 10 }$ 
C)  $- 6 - \sqrt { 10 } , - 6 + \sqrt { 10 }$ 
D)  $6 - \sqrt { 26 } , 6 + \sqrt { 26 }$

Question 3

Use the discriminant to determine the number and type of solutions of the equation.
-$5 - 4 x ^ { 2 } = - 6 x + 3$

Accepted Answer

A)  two complex but not real solutions 
B)  one real solution 
C)  two real solutions 
A)  two complex but not real solutions 
B)  one real solution 
C)  two real solutions

Question 4

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$\frac { ( x - 1 ) ( 3 - x ) } { ( x - 2 ) ^ { 2 } } \leq 0$

Accepted Answer

A)  $( - \infty , - 3 ] \cup ( - 2 , - 1 ) \cup [ 1 , \infty )$
  
B)  $( - \infty , 1 ) \cup ( 3 , \infty )$
  
C)  $( - \infty , 1 ] \cup [ 3 , \infty )$
  
D)  $( - \infty , - 3 ) \cup ( - 1 , \infty )$
  
A)  $( - \infty , - 3 ] \cup ( - 2 , - 1 ) \cup [ 1 , \infty )$
  
B)  $( - \infty , 1 ) \cup ( 3 , \infty )$
  
C)  $( - \infty , 1 ] \cup [ 3 , \infty )$
  
D)  $( - \infty , - 3 ) \cup ( - 1 , \infty )$

Question 5

Solve.
-Two pipes can be used to fill a pool. Working together, the two pipes can fill the pool in 2 hours. The larger pipe can fill the pool in 3 hours less time than the smaller pipe can alone. Find the time To the nearest tenth of an hour it takes for the smaller pipe working alone to fill the pool.

Accepted Answer

A)  6.0 hr 
B)  3.1 hr 
C)  3.0 hr 
D)  6.1 hr 
A)  6.0 hr 
B)  3.1 hr 
C)  3.0 hr 
D)  6.1 hr

Question 6

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

Accepted Answer

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

Question 7

Find all numbers that satisfy the following.
-A number minus the product of 49 and its reciprocal is less than zero. Find the numbers.

Accepted Answer

A)  any number between $- 7$ and 7 
B)  any number less than 7 
C)  any number between 0 and 7 
D)  any number less than $- 7$ or between 0 and 7 
A)  any number between $- 7$ and 7 
B)  any number less than 7 
C)  any number between 0 and 7 
D)  any number less than $- 7$ or between 0 and 7

Question 8

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$\frac { x } { x + 4 } \geq 2$

Accepted Answer

A) $(-\infty,-4) \cup[0, \infty)$
  
B)  $( - \infty , - 8 ] \cup ( - 4 , \infty )$
  
C) $( - 4,8 ]$
  
D)  $[ - 8 , - 4 )$
  
A) $(-\infty,-4) \cup[0, \infty)$
  
B)  $( - \infty , - 8 ] \cup ( - 4 , \infty )$
  
C) $( - 4,8 ]$
  
D)  $[ - 8 , - 4 )$

Question 9

Solve.
-The diagonal of a rectangular storage room is 12 yards long. If its length is 4 times its width, find the dimensions of the room.

Accepted Answer

A)  $\frac { \sqrt { 17 } } { 17 }$ yd by $\frac { 4 \sqrt { 17 } } { 17 } \mathrm { yd }$ 
B)  $\frac { 4 \sqrt { 17 } } { 17 }$ yd by $\frac { 16 \sqrt { 17 } } { 17 } \mathrm { yd }$ 
C)  $\frac { 12 \sqrt { 17 } } { 17 } \mathrm { yd }$ by $\frac { 48 \sqrt { 17 } } { 17 } \mathrm { yd }$ 
D)  $12 \sqrt { 17 } \mathrm { yd }$ by $48 \sqrt { 17 } \mathrm { yd }$ 
A)  $\frac { \sqrt { 17 } } { 17 }$ yd by $\frac { 4 \sqrt { 17 } } { 17 } \mathrm { yd }$ 
B)  $\frac { 4 \sqrt { 17 } } { 17 }$ yd by $\frac { 16 \sqrt { 17 } } { 17 } \mathrm { yd }$ 
C)  $\frac { 12 \sqrt { 17 } } { 17 } \mathrm { yd }$ by $\frac { 48 \sqrt { 17 } } { 17 } \mathrm { yd }$ 
D)  $12 \sqrt { 17 } \mathrm { yd }$ by $48 \sqrt { 17 } \mathrm { yd }$

Question 10

Use the quadratic formula to solve the equation.
-$x ^ { 2 } + 14 x + 58 = 0$

Accepted Answer

A)  $- 7 - 9 i , - 7 + 9 i$ 
B)  $- 7 + 3 \mathrm { i }$ 
C)  $- 10 , - 4$ 
D)  $- 7 - 3 i , - 7 + 3 i$ 
A)  $- 7 - 9 i , - 7 + 9 i$ 
B)  $- 7 + 3 \mathrm { i }$ 
C)  $- 10 , - 4$ 
D)  $- 7 - 3 i , - 7 + 3 i$

Question 11

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

Accepted Answer

A)  $8 , - \mathrm { i } , \mathrm { i }$ 
B)  $- 8 , - \mathrm { i } , \mathrm { i }$ 
C)  $- 1,1 , - 8 i , 8 i$ 
D)  $- 1,1 , - 8,8$ 
A)  $8 , - \mathrm { i } , \mathrm { i }$ 
B)  $- 8 , - \mathrm { i } , \mathrm { i }$ 
C)  $- 1,1 , - 8 i , 8 i$ 
D)  $- 1,1 , - 8,8$

Question 12

Solve the equation.
-$5 x ^ { 2 } + 6 x + 1 = 0$

Accepted Answer

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

Question 13

Solve the equation.
-$2 x ^ { 2 } - 5 x = 7$

Accepted Answer

A)  $\frac { 2 } { 7 } , 1$ 
B)  $\frac { 7 } { 2 } , - 1$ 
C)  $\frac { 7 } { 2 } , 1$ 
D)  $\frac { 2 } { 7 } , - 1$ 
A)  $\frac { 2 } { 7 } , 1$ 
B)  $\frac { 7 } { 2 } , - 1$ 
C)  $\frac { 7 } { 2 } , 1$ 
D)  $\frac { 2 } { 7 } , - 1$

Question 14

Solve.
-$\frac { 2 } { x } + \frac { 3 } { x - 5 } = 1$

Accepted Answer

A)  $5 - \sqrt { 35 } , 5 + \sqrt { 35 }$ 
B)  $- 5 - \sqrt { 35 } , - 5 + \sqrt { 35 }$ 
C)  $- 5 - \sqrt { 15 } , - 5 + \sqrt { 15 }$ 
D)  $5 - \sqrt { 15 } , 5 + \sqrt { 15 }$ 
A)  $5 - \sqrt { 35 } , 5 + \sqrt { 35 }$ 
B)  $- 5 - \sqrt { 35 } , - 5 + \sqrt { 35 }$ 
C)  $- 5 - \sqrt { 15 } , - 5 + \sqrt { 15 }$ 
D)  $5 - \sqrt { 15 } , 5 + \sqrt { 15 }$

Question 15

Use the square root property to solve the equation.
-$( 14 - 13 x ) ^ { 2 } = 85$

Accepted Answer

A)  $\frac { 13 - \sqrt { 85 } } { 14 } , \frac { 13 + \sqrt { 85 } } { 14 }$ 
B)  $\frac { 99 } { 13 } , - \frac { 71 } { 13 }$ 
C)  $\frac { \sqrt { 85 - 14 } } { 13 } , \frac { \sqrt { 85 + 14 } } { 13 }$ 
D)  $\frac { 14 - \sqrt { 85 } } { 13 } , \frac { 14 + \sqrt { 85 } } { 13 }$ 
A)  $\frac { 13 - \sqrt { 85 } } { 14 } , \frac { 13 + \sqrt { 85 } } { 14 }$ 
B)  $\frac { 99 } { 13 } , - \frac { 71 } { 13 }$ 
C)  $\frac { \sqrt { 85 - 14 } } { 13 } , \frac { \sqrt { 85 + 14 } } { 13 }$ 
D)  $\frac { 14 - \sqrt { 85 } } { 13 } , \frac { 14 + \sqrt { 85 } } { 13 }$

Question 16

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$x ^ { 4 } - 40 x ^ { 2 } + 144 \geq 0$

Accepted Answer

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

Question 17

Solve.
-Because of the increase in traffic between Springfield and Orangeville, a new road was built to connect the two towns. The old road goes south x miles from Springfield to Freeport and then goes
East x + 5 miles from Freeport to Orangeville. The new road is 9 miles long and goes straight from
Springfield to Orangeville. Find the number of miles that a person saves by driving the new road

Accepted Answer

A)  $\left( \frac { 5 } { 2 } + \frac { \sqrt { 137 } } { 2 } \right) \mathrm { mi }$ 
B)  $( \sqrt { 137 } + 9 ) \mathrm { mi }$ 
C)  $\left( - \frac { 5 } { 2 } + \frac { \sqrt { 137 } } { 2 } \right) \mathrm { mi }$ 
D)  $( \sqrt { 137 } - 9 ) \mathrm { mi }$ 
A)  $\left( \frac { 5 } { 2 } + \frac { \sqrt { 137 } } { 2 } \right) \mathrm { mi }$ 
B)  $( \sqrt { 137 } + 9 ) \mathrm { mi }$ 
C)  $\left( - \frac { 5 } { 2 } + \frac { \sqrt { 137 } } { 2 } \right) \mathrm { mi }$ 
D)  $( \sqrt { 137 } - 9 ) \mathrm { mi }$

Question 18

Solve.
-The hypotenuse of a right triangle is 9 feet long. One leg of the triangle is 5 feet longer then the other leg. Find the perimeter of the triangle.

Accepted Answer

A)  $( \sqrt { 137 } + 9 ) \mathrm { ft }$ 
B)  $\left( \frac { 5 } { 2 } + \frac { \sqrt { 137 } } { 2 } \right) \mathrm { ft }$ 
C)  $( \sqrt { 137 } - 9 ) \mathrm { ft }$ 
D)  $\left( - \frac { 5 } { 2 } + \frac { \sqrt { 137 } } { 2 } \right) \mathrm { ft }$ 
A)  $( \sqrt { 137 } + 9 ) \mathrm { ft }$ 
B)  $\left( \frac { 5 } { 2 } + \frac { \sqrt { 137 } } { 2 } \right) \mathrm { ft }$ 
C)  $( \sqrt { 137 } - 9 ) \mathrm { ft }$ 
D)  $\left( - \frac { 5 } { 2 } + \frac { \sqrt { 137 } } { 2 } \right) \mathrm { ft }$

Question 19

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$\left( x ^ { 2 } - 36 \right) \left( x ^ { 2 } - 4 \right) > 0$

Accepted Answer

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

Question 20

Solve.
-$x ^ { 3 } - 125 = 0$

Accepted Answer

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

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } - 6 x \geq - 8$

Solve the equation by completing the square. - $x ^ { 2 } + 12 x = - 26$

Use the discriminant to determine the number and type of solutions of the equation. - $5 - 4 x ^ { 2 } = - 6 x + 3$

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

Find all numbers that satisfy the following. -A number minus the product of 49 and its reciprocal is less than zero. Find the numbers.

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $\frac { x } { x + 4 } \geq 2$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - \frac { x } { x + 4 } \geq 2$

Solve. -The diagonal of a rectangular storage room is 12 yards long. If its length is 4 times its width, find the dimensions of the room.

Use the quadratic formula to solve the equation. - $x ^ { 2 } + 14 x + 58 = 0$

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

Solve the equation. - $5 x ^ { 2 } + 6 x + 1 = 0$

Solve the equation. - $2 x ^ { 2 } - 5 x = 7$

Solve. - $\frac { 2 } { x } + \frac { 3 } { x - 5 } = 1$

Use the square root property to solve the equation. - $( 14 - 13 x ) ^ { 2 } = 85$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $x ^ { 4 } - 40 x ^ { 2 } + 144 \geq 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - x ^ { 4 } - 40 x ^ { 2 } + 144 \geq 0$

Solve. -The hypotenuse of a right triangle is 9 feet long. One leg of the triangle is 5 feet longer then the other leg. Find the perimeter of the triangle.

Solve. - $x ^ { 3 } - 125 = 0$

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. Write the solution set in interval notation. - x2−6x≥−8x ^ { 2 } - 6 x \geq - 8x2−6x≥−8

Solve the equation by completing the square. - x2+12x=−26x ^ { 2 } + 12 x = - 26x2+12x=−26

Use the discriminant to determine the number and type of solutions of the equation. - 5−4x2=−6x+35 - 4 x ^ { 2 } = - 6 x + 35−4x2=−6x+3

Solve the inequality. Graph the solution set and write the solution set in interval notation. - (x−1)(3−x)(x−2)2≤0\frac { ( x - 1 ) ( 3 - x ) } { ( x - 2 ) ^ { 2 } } \leq 0(x−2)2(x−1)(3−x)​≤0

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