Question 1

Graph the solution to the inequality on the real number line. $x ^ { 2 } - 6 x + 6 > 0$

Accepted Answer

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

Question 2

Graph the solution to the inequality on the real number line. $x ( x + 3 ) ( x - 3 ) > 0$

Accepted Answer

A)    
B)    
C)    
D)    
E) none of these 
A)    
B)    
C)    
D)    
E) none of these

Question 3

Find all real and complex solutions of the quadratic equation $x ^ { 2 } + 256 = 0$ .

Accepted Answer

A)  -256 
B)  $\pm 256 i$ 
C)  $\pm 16$ 
D)  $\pm 16 i$ 
E)  $16 i$ 
A)  -256 
B)  $\pm 256 i$ 
C)  $\pm 16$ 
D)  $\pm 16 i$ 
E)  $16 i$

Question 4

Find all real and complex solutions of the quadratic equation $6 x ^ { 2 } - 5 x = 0$.

Accepted Answer

A)  $0,\frac { 5 } { 6 }$ 
B)  $0 , \frac { 5 } { 6 } i$ 
C)  $\frac { 36 } { 5 }$ 
D)  $\frac { 5 } { 6 } i$ 
E)  $0 , \frac { 6 } { 5 }$ 
A)  $0,\frac { 5 } { 6 }$ 
B)  $0 , \frac { 5 } { 6 } i$ 
C)  $\frac { 36 } { 5 }$ 
D)  $\frac { 5 } { 6 } i$ 
E)  $0 , \frac { 6 } { 5 }$

Question 5

Solve the equation $\left( x ^ { 2 } - 13 \right) ^ { 2 } + 3 \left( x ^ { 2 } - 13 \right) - 4 = 0$ . (Find all real and complex solutions.)

Accepted Answer

A)  $\pm 3 , \pm \sqrt { 14 } i$ 
B)  $\pm 13 , \pm \sqrt { 14 } i$ 
C)  $\pm 3 , \pm \sqrt { 14 }$ 
D)  $\pm 13 , \pm 14 i$ 
E)  $\pm 9 , \pm 14$ 
A)  $\pm 3 , \pm \sqrt { 14 } i$ 
B)  $\pm 13 , \pm \sqrt { 14 } i$ 
C)  $\pm 3 , \pm \sqrt { 14 }$ 
D)  $\pm 13 , \pm 14 i$ 
E)  $\pm 9 , \pm 14$

Question 6

Graph $y = - \frac { 1 } { 2 } x ^ { 2 } + 2 x - 2$ .

Accepted Answer

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

Question 7

Solve the equation $7 x ^ { 2 } = 63$ by using the Square Root Property.

Accepted Answer

A)  $\pm 7$ 
B)  $\pm 3$ 
C)  $\pm 9$ 
D)  $7,3$ 
E)  9 
A)  $\pm 7$ 
B)  $\pm 3$ 
C)  $\pm 9$ 
D)  $7,3$ 
E)  9

Question 8

Find the critical numbers. $y ( y - 7 ) - 9 ( y - 7 )$

Accepted Answer

A)  $- 7 , - 9$ 
B)  $7,9$ 
C)  $0,7$ 
D)  $7 , - 9$ 
E)  $0 , - 7$ 
A)  $- 7 , - 9$ 
B)  $7,9$ 
C)  $0,7$ 
D)  $7 , - 9$ 
E)  $0 , - 7$

Question 9

The height y in feet of a ball thrown by a child is modeled by $y = - 0.1 x ^ { 2 } + 2.5 x + 5$ , where x is the horizontal distance in feet from where the ball is thrown. What is the maximum height of the ball? Round your answer to the nearest integer.

Accepted Answer

A)  7 feet 
B)  11 feet 
C)  21 feet 
D)  35 feet 
E)  52 feet 
A)  7 feet 
B)  11 feet 
C)  21 feet 
D)  35 feet 
E)  52 feet

Question 10

The height y in feet of a ball thrown by a child is modeled by $y = - 0.1 x ^ { 2 } + 7 x + 4$ , where x is the horizontal distance in feet from where the ball is thrown. How high is the ball when it leaves the child s hand?

Accepted Answer

A)  0.4 foot 
B) 0.1 foot 
C)  13.9 feet 
D)  11 feet 
E)  4 feet 
A)  0.4 foot 
B) 0.1 foot 
C)  13.9 feet 
D)  11 feet 
E)  4 feet

Question 11

Sketch the parabola given by $y = - 2 x ^ { 2 } - 12 x - 21$ and then identify its vertex.

Accepted Answer

A) vertex: (-2,-2)    
B) vertex: (3,4)   
C) vertex: (-2,-3)  
  
D) vertex: (2,4)   
E) vertex: (-3,-3)
  
A) vertex: (-2,-2)    
B) vertex: (3,4)   
C) vertex: (-2,-3)  
  
D) vertex: (2,4)   
E) vertex: (-3,-3)

Question 12

Determine all real values of x for which the function $7 x ^ { 2 } - 13 x + 1$ has the value 3.

Accepted Answer

A)  $- \frac { 13 } { 7 } \pm \frac { 13 \sqrt { 57 } } { 14 }$ 
B)  $\frac { 13 } { 14 } \pm \frac { \sqrt { 57 } } { 14 }$ 
C)  $\frac { 13 } { 7 } \pm \frac { 13 \sqrt { 57 } } { 7 }$ 
D)  $\frac { 13 } { 7 } \pm \frac { \sqrt { 57 } } { 14 }$ 
E)  $- \frac { 13 } { 14 } \pm \frac { \sqrt { 57 } } { 7 }$ 
A)  $- \frac { 13 } { 7 } \pm \frac { 13 \sqrt { 57 } } { 14 }$ 
B)  $\frac { 13 } { 14 } \pm \frac { \sqrt { 57 } } { 14 }$ 
C)  $\frac { 13 } { 7 } \pm \frac { 13 \sqrt { 57 } } { 7 }$ 
D)  $\frac { 13 } { 7 } \pm \frac { \sqrt { 57 } } { 14 }$ 
E)  $- \frac { 13 } { 14 } \pm \frac { \sqrt { 57 } } { 7 }$

Question 13

Graph the solution to the inequality on the real line. $\frac { 3 } { x - 6 } \geq - 1$

Accepted Answer

A)    
B)    
C)    
D)    
E) none of these 
A)    
B)    
C)    
D)    
E) none of these

Question 14

A service organization buys a block of tickets to a hockey game for $139 . After 5 more people decide to go to the game, the price per ticket is decreased by $1. How many people are going to the game?

Accepted Answer

A)  24 people 
B)  34 people 
C)  29 people 
D)  $53$ people 
E)  $32$ people 
A)  24 people 
B)  34 people 
C)  29 people 
D)  $53$ people 
E)  $32$ people

Question 15

An office contains two printers. Printer B takes 5 minutes longer than printer A to print the company s monthly financial report. With the two printers working, it takes 3.5 minutes to complete the report. How long (in minutes)would it take each printer individually to complete the report? Round your answer to two decimal places.

Accepted Answer

A) Printer A: 4.12 minutes, Printer B: 10.12 minutes 
B) Printer A: 2.65 minutes, Printer B: 8.65 minutes 
C) Printer A: 5.3 minutes, Printer B: 10.3 minutes 
D) Printer A: 5.3 minutes, Printer B: 5.3 minutes 
E) Printer A: 6.3 minutes, Printer B: 10.12 minutes 
A) Printer A: 4.12 minutes, Printer B: 10.12 minutes 
B) Printer A: 2.65 minutes, Printer B: 8.65 minutes 
C) Printer A: 5.3 minutes, Printer B: 10.3 minutes 
D) Printer A: 5.3 minutes, Printer B: 5.3 minutes 
E) Printer A: 6.3 minutes, Printer B: 10.12 minutes

Question 16

Match the equation $y = ( x + 1 ) ^ { 2 } + 3$ with its graph.

Accepted Answer

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

Question 17

Write $x ( 4 - x ) = 14$ in general form.

Accepted Answer

A)  $x ^ { 2 } + 4 x - 14 = 0$ 
B)  $x ^ { 2 } - 4 x + 14 = 0$ 
C)  $( 4 - x ) = \frac { 14 } { x ^ { 2 } }$ 
D)  $3 x - 14 = 0$ 
E)  $x ^ { 2 } + 4 x + 14 = 0$ 
A)  $x ^ { 2 } + 4 x - 14 = 0$ 
B)  $x ^ { 2 } - 4 x + 14 = 0$ 
C)  $( 4 - x ) = \frac { 14 } { x ^ { 2 } }$ 
D)  $3 x - 14 = 0$ 
E)  $x ^ { 2 } + 4 x + 14 = 0$

Question 18

The height y (in feet)of a ball that you throw is given by $y = - \frac { 1 } { 190 } x ^ { 2 } + x + 5$ where x is the horizontal distance (in feet)from where you release the ball. How high is the ball when you release it?

Accepted Answer

A)  5 feet 
B)  2.5 feet 
C)  1 foot 
D)  99 feet 
E)  $100$ feet 
A)  5 feet 
B)  2.5 feet 
C)  1 foot 
D)  99 feet 
E)  $100$ feet

Question 19

Write the equation of the parabola in standard form and find the vertex of its graph. $y = x ^ { 2 } + 10 x + 16$

Accepted Answer

A)  $y = ( x + 5 ) ^ { 2 } - 9$ ; vertex: $( 5 , - 41 )$ 
B)  $y = ( x - 5 ) ^ { 2 } + 11$ ; vertex: $( 5,41 )$ 
C)  $y = ( x + 8 ) ( x + 2 )$ ; vertex: $( 10,16 )$ 
D)  $y = ( x + 5 ) ^ { 2 } - 9$ ; vertex: $( - 5 , - 9 )$ 
E)  $y = ( x + 5 ) ^ { 2 } + 41$ ; vertex: $( - 5,41 )$ 
A)  $y = ( x + 5 ) ^ { 2 } - 9$ ; vertex: $( 5 , - 41 )$ 
B)  $y = ( x - 5 ) ^ { 2 } + 11$ ; vertex: $( 5,41 )$ 
C)  $y = ( x + 8 ) ( x + 2 )$ ; vertex: $( 10,16 )$ 
D)  $y = ( x + 5 ) ^ { 2 } - 9$ ; vertex: $( - 5 , - 9 )$ 
E)  $y = ( x + 5 ) ^ { 2 } + 41$ ; vertex: $( - 5,41 )$

Question 20

Solve $2 y ( y - 16 ) + 5 ( y - 16 ) = 0$ .

Accepted Answer

A)  $y = 16 , y = - 5$ 
B)  $y = - 16 , y = \frac { 2 } { 5 }$ 
C)  $y = 16 , y = - \frac { 5 } { 2 }$ 
D)  $y = 16 , y = - \frac { 2 } { 5 }$ 
E)  $y = - 16 , y = - \frac { 5 } { 2 }$ 
A)  $y = 16 , y = - 5$ 
B)  $y = - 16 , y = \frac { 2 } { 5 }$ 
C)  $y = 16 , y = - \frac { 5 } { 2 }$ 
D)  $y = 16 , y = - \frac { 2 } { 5 }$ 
E)  $y = - 16 , y = - \frac { 5 } { 2 }$

Graph the solution to the inequality on the real number line. $x ^ { 2 } - 6 x + 6 > 0$

Graph the solution to the inequality on the real number line. $x ( x + 3 ) ( x - 3 ) > 0$

Find all real and complex solutions of the quadratic equation $x ^ { 2 } + 256 = 0$ .

Find all real and complex solutions of the quadratic equation $6 x ^ { 2 } - 5 x = 0$ .

Solve the equation $\left( x ^ { 2 } - 13 \right) ^ { 2 } + 3 \left( x ^ { 2 } - 13 \right) - 4 = 0$ . (Find all real and complex solutions.)

Graph $y = - \frac { 1 } { 2 } x ^ { 2 } + 2 x - 2$ .

Solve the equation $7 x ^ { 2 } = 63$ by using the Square Root Property.

Find the critical numbers. $y ( y - 7 ) - 9 ( y - 7 )$

The height y in feet of a ball thrown by a child is modeled by $y = - 0.1 x ^ { 2 } + 2.5 x + 5$ , where x is the horizontal distance in feet from where the ball is thrown. What is the maximum height of the ball? Round your answer to the nearest integer.

The height y in feet of a ball thrown by a child is modeled by $y = - 0.1 x ^ { 2 } + 7 x + 4$ , where x is the horizontal distance in feet from where the ball is thrown. How high is the ball when it leaves the child s hand?

Sketch the parabola given by $y = - 2 x ^ { 2 } - 12 x - 21$ and then identify its vertex.

Determine all real values of x for which the function $7 x ^ { 2 } - 13 x + 1$ has the value 3.

Graph the solution to the inequality on the real line. $\frac { 3 } { x - 6 } \geq - 1$

A service organization buys a block of tickets to a hockey game for $139 . After 5 more people decide to go to the game, the price per ticket is decreased by $1. How many people are going to the game?

Match the equation $y = ( x + 1 ) ^ { 2 } + 3$ with its graph.

Write $x ( 4 - x ) = 14$ in general form.

The height y (in feet)of a ball that you throw is given by $y = - \frac { 1 } { 190 } x ^ { 2 } + x + 5$ where x is the horizontal distance (in feet)from where you release the ball. How high is the ball when you release it?

Write the equation of the parabola in standard form and find the vertex of its graph. $y = x ^ { 2 } + 10 x + 16$

Solve $2 y ( y - 16 ) + 5 ( y - 16 ) = 0$ .

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Exam 8: Quadratic Equations, Functions, and Inequalities

Graph the solution to the inequality on the real number line. x2−6x+6>0x ^ { 2 } - 6 x + 6 > 0x2−6x+6>0

Graph the solution to the inequality on the real number line. x(x+3)(x−3)>0x ( x + 3 ) ( x - 3 ) > 0x(x+3)(x−3)>0

Find all real and complex solutions of the quadratic equation x2+256=0x ^ { 2 } + 256 = 0x2+256=0 .

Find all real and complex solutions of the quadratic equation 6x2−5x=06 x ^ { 2 } - 5 x = 06x2−5x=0 .

Solve the equation (x2−13)2+3(x2−13)−4=0\left( x ^ { 2 } - 13 \right) ^ { 2 } + 3 \left( x ^ { 2 } - 13 \right) - 4 = 0(x2−13)2+3(x2−13)−4=0 . (Find all real and complex solutions.)

Graph y=−12x2+2x−2y = - \frac { 1 } { 2 } x ^ { 2 } + 2 x - 2y=−21​x2+2x−2 .

Solve the equation 7x2=637 x ^ { 2 } = 637x2=63 by using the Square Root Property.

Find the critical numbers. y(y−7)−9(y−7)y ( y - 7 ) - 9 ( y - 7 )y(y−7)−9(y−7)

The height y in feet of a ball thrown by a child is modeled by y=−0.1x2+2.5x+5y = - 0.1 x ^ { 2 } + 2.5 x + 5y=−0.1x2+2.5x+5 , where x is the horizontal distance in feet from where the ball is thrown. What is the maximum height of the ball? Round your answer to the nearest integer.

The height y in feet of a ball thrown by a child is modeled by y=−0.1x2+7x+4y = - 0.1 x ^ { 2 } + 7 x + 4y=−0.1x2+7x+4 , where x is the horizontal distance in feet from where the ball is thrown. How high is the ball when it leaves the child s hand?

Sketch the parabola given by y=−2x2−12x−21y = - 2 x ^ { 2 } - 12 x - 21y=−2x2−12x−21 and then identify its vertex.

Determine all real values of x for which the function 7x2−13x+17 x ^ { 2 } - 13 x + 17x2−13x+1 has the value 3.

Graph the solution to the inequality on the real line. 3x−6≥−1\frac { 3 } { x - 6 } \geq - 1x−63​≥−1

A service organization buys a block of tickets to a hockey game for $139 . After 5 more people decide to go to the game, the price per ticket is decreased by $1. How many people are going to the game?

Match the equation y=(x+1)2+3y = ( x + 1 ) ^ { 2 } + 3y=(x+1)2+3 with its graph.

Write x(4−x)=14x ( 4 - x ) = 14x(4−x)=14 in general form.

The height y (in feet)of a ball that you throw is given by y=−1190x2+x+5y = - \frac { 1 } { 190 } x ^ { 2 } + x + 5y=−1901​x2+x+5 where x is the horizontal distance (in feet)from where you release the ball. How high is the ball when you release it?

Write the equation of the parabola in standard form and find the vertex of its graph. y=x2+10x+16y = x ^ { 2 } + 10 x + 16y=x2+10x+16

Solve 2y(y−16)+5(y−16)=02 y ( y - 16 ) + 5 ( y - 16 ) = 02y(y−16)+5(y−16)=0 .

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Graph the solution to the inequality on the real number line. $x ^ { 2 } - 6 x + 6 > 0$

Graph the solution to the inequality on the real number line. $x ( x + 3 ) ( x - 3 ) > 0$

Find all real and complex solutions of the quadratic equation $x ^ { 2 } + 256 = 0$ .

Find all real and complex solutions of the quadratic equation $6 x ^ { 2 } - 5 x = 0$ .

Solve the equation $\left( x ^ { 2 } - 13 \right) ^ { 2 } + 3 \left( x ^ { 2 } - 13 \right) - 4 = 0$ . (Find all real and complex solutions.)

Graph $y = - \frac { 1 } { 2 } x ^ { 2 } + 2 x - 2$ .

Solve the equation $7 x ^ { 2 } = 63$ by using the Square Root Property.

Find the critical numbers. $y ( y - 7 ) - 9 ( y - 7 )$

The height y in feet of a ball thrown by a child is modeled by $y = - 0.1 x ^ { 2 } + 2.5 x + 5$ , where x is the horizontal distance in feet from where the ball is thrown. What is the maximum height of the ball? Round your answer to the nearest integer.

The height y in feet of a ball thrown by a child is modeled by $y = - 0.1 x ^ { 2 } + 7 x + 4$ , where x is the horizontal distance in feet from where the ball is thrown. How high is the ball when it leaves the child s hand?

Sketch the parabola given by $y = - 2 x ^ { 2 } - 12 x - 21$ and then identify its vertex.

Determine all real values of x for which the function $7 x ^ { 2 } - 13 x + 1$ has the value 3.

Graph the solution to the inequality on the real line. $\frac { 3 } { x - 6 } \geq - 1$

Match the equation $y = ( x + 1 ) ^ { 2 } + 3$ with its graph.

Write $x ( 4 - x ) = 14$ in general form.

The height y (in feet)of a ball that you throw is given by $y = - \frac { 1 } { 190 } x ^ { 2 } + x + 5$ where x is the horizontal distance (in feet)from where you release the ball. How high is the ball when you release it?

Write the equation of the parabola in standard form and find the vertex of its graph. $y = x ^ { 2 } + 10 x + 16$

Solve $2 y ( y - 16 ) + 5 ( y - 16 ) = 0$ .