Question 1

Sketch the graph of  $h ( x ) = - ( x + 4 ) ^ { 2 }$ .

Accepted Answer

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

Question 2

Solve $t ^ { 2 } + 7 t = 0$ by factoring.

Accepted Answer

A)  $t = 0 , t = 7$ 
B)  t=0 
C)  $t = 0 , t = - 7$ 
D)  $t = 0 , t = \frac { 7 } { 2 }$ 
E)  t=-7 
A)  $t = 0 , t = 7$ 
B)  t=0 
C)  $t = 0 , t = - 7$ 
D)  $t = 0 , t = \frac { 7 } { 2 }$ 
E)  t=-7

Question 3

Determine the intervals for which $4 x ( x - 5 )$ is entirely negative and entirely positive.

Accepted Answer

A) negative: $( 0,5 )$ positive: $( - \infty , 0 ) , ( 5 , \infty )$ 
B) negative: $( - \infty , - 5 ) , ( 5 , \infty )$ positive: $( - 5,5 )$ 
C) negative: $( - \infty , 0 ) , ( 1.25 , \infty )$ positive: $( 0,1.25 )$ 
D) negative: $( 0,1.25 )$ positive: $( - \infty , 0 ) , ( 1.25 , \infty )$ 
E) negative: $( - \infty , 0 ) , ( 5 , \infty )$ positive: $( 0,5 )$ 
A) negative: $( 0,5 )$ positive: $( - \infty , 0 ) , ( 5 , \infty )$ 
B) negative: $( - \infty , - 5 ) , ( 5 , \infty )$ positive: $( - 5,5 )$ 
C) negative: $( - \infty , 0 ) , ( 1.25 , \infty )$ positive: $( 0,1.25 )$ 
D) negative: $( 0,1.25 )$ positive: $( - \infty , 0 ) , ( 1.25 , \infty )$ 
E) negative: $( - \infty , 0 ) , ( 5 , \infty )$ positive: $( 0,5 )$

Question 4

Determine the intervals for which $x ^ { 2 } - 4 x - 45$ is entirely negative and entirely positive.

Accepted Answer

A) negative: $( 5,9 )$ ; positive: $( - \infty , 5 ) \cup ( 9 , \infty )$ 
B) negative: $( - 5,9 )$ ; positive: $( - \infty , - 9 ) \cup ( 5 , \infty )$ 
C) negative: $( - 5,9 )$ ; positive: $( - \infty , - 5 ) \cup ( 9 , \infty )$ 
D) negative: $( 5,9 )$ ; positive: $( - \infty , - 9 ) \cup ( 5 , \infty )$ 
E) negative: $( - 9,5 )$ ; positive: $( - \infty , - 9 ) \cup ( 5 , \infty )$ 
A) negative: $( 5,9 )$ ; positive: $( - \infty , 5 ) \cup ( 9 , \infty )$ 
B) negative: $( - 5,9 )$ ; positive: $( - \infty , - 9 ) \cup ( 5 , \infty )$ 
C) negative: $( - 5,9 )$ ; positive: $( - \infty , - 5 ) \cup ( 9 , \infty )$ 
D) negative: $( 5,9 )$ ; positive: $( - \infty , - 9 ) \cup ( 5 , \infty )$ 
E) negative: $( - 9,5 )$ ; positive: $( - \infty , - 9 ) \cup ( 5 , \infty )$

Question 5

Find the critical numbers. $\frac { 4 } { x - 3 }$

Accepted Answer

A)  $- \frac { 4 } { 3 }$ 
B)  $7$ 
C)  $4,3$ 
D)  $- 3$ 
E)  $3$ 
A)  $- \frac { 4 } { 3 }$ 
B)  $7$ 
C)  $4,3$ 
D)  $- 3$ 
E)  $3$

Question 6

The height h (in feet)of an object dropped from a tower 54 feet high is modeled by $h = 54 - 16 t ^ { 2 }$ , where t is the time in seconds. How long does it take for the object to reach the ground? Round your answer to two decimal places.

Accepted Answer

A) 3.86 seconds 
B) 3.67 seconds 
C) 0.46 second 
D) 1.84 seconds 
E) 6.16 seconds 
A) 3.86 seconds 
B) 3.67 seconds 
C) 0.46 second 
D) 1.84 seconds 
E) 6.16 seconds

Question 7

Use a graphing calculator to solve the inequality $x ^ { 2 } + 12 x + 32 \geq 92$ . Round all numerical values in your answer to three decimal places, where applicable.

Accepted Answer

A)  $( - \infty , - 5.798 ] \cup [ 13.798 , \infty )$ 
B)  $( 0 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , - 15.798 ] \cup [ 3.798 , \infty )$ 
E)  $( - \infty , - 13.798 ] \cup [ 5.798 , \infty )$ 
A)  $( - \infty , - 5.798 ] \cup [ 13.798 , \infty )$ 
B)  $( 0 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , - 15.798 ] \cup [ 3.798 , \infty )$ 
E)  $( - \infty , - 13.798 ] \cup [ 5.798 , \infty )$

Question 8

Solve the inequality $\frac { x - 1 } { x - 5 } \leq 3$ and graph the solution on the real number line.

Accepted Answer

A) Solution: $( 5 , \infty )$   
B) Solution: $( 0 , \infty )$   
C) Solution: $( - \infty , 0 ) \cup [ 7 , \infty )$   
D) Solution: $( - \infty , 5 ) \cup [ 7 , \infty )$   
E) Solution: $( - \infty , \infty )$   
A) Solution: $( 5 , \infty )$   
B) Solution: $( 0 , \infty )$   
C) Solution: $( - \infty , 0 ) \cup [ 7 , \infty )$   
D) Solution: $( - \infty , 5 ) \cup [ 7 , \infty )$   
E) Solution: $( - \infty , \infty )$

Question 9

Graph the solution to the inequality on the real line. $\frac { 4 } { x - 4 } > 0$

Accepted Answer

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

Question 10

Find the intercepts of  $y = 9 x ^ { 2 } - 8 x + 8$ .

Accepted Answer

A) x -intercept: $\left( - \frac { 4 } { 9 } , 0 \right)$ y -intercepts: (0,8) 
B) no x -intercepts y -intercept: (0,8) 
C) x -intercept: (8,0) no y -intercepts 
D) no x -intercepts y -intercept: (0,-8) 
E) x -intercept: (8,0) y -intercept: (0,8) 
A) x -intercept: $\left( - \frac { 4 } { 9 } , 0 \right)$ y -intercepts: (0,8) 
B) no x -intercepts y -intercept: (0,8) 
C) x -intercept: (8,0) no y -intercepts 
D) no x -intercepts y -intercept: (0,-8) 
E) x -intercept: (8,0) y -intercept: (0,8)

Question 11

What term should be added to $y ^ { 2 } - \frac { 1 } { 5 } y$ to make it a perfect square trinomial?

Accepted Answer

A)  5 
B)  $\frac { 1 } { 100 }$ 
C)  100 
D)  $ \frac{5}{2} $ 
E)  $\frac { 1 } { 50 }$ 
A)  5 
B)  $\frac { 1 } { 100 }$ 
C)  100 
D)  $ \frac{5}{2} $ 
E)  $\frac { 1 } { 50 }$

Question 12

Solve the equation by using the Square Root Property. $( 2 x + 2 ) ^ { 2 } = - 17$

Accepted Answer

A)  $x = \pm \sqrt { \frac { 19 } { 2 } } i$ 
B)  $x = \frac { - 2 \pm \sqrt { 17 } i } { 2 }$ 
C)  $x = \pm \frac { \sqrt { 17 } i } { 2 } - 2$ 
D)  $x = \frac { \pm 2 + \sqrt { 17 } i } { 2 }$ 
E)  $x = 2 \pm \sqrt { 17 } i$ 
A)  $x = \pm \sqrt { \frac { 19 } { 2 } } i$ 
B)  $x = \frac { - 2 \pm \sqrt { 17 } i } { 2 }$ 
C)  $x = \pm \frac { \sqrt { 17 } i } { 2 } - 2$ 
D)  $x = \frac { \pm 2 + \sqrt { 17 } i } { 2 }$ 
E)  $x = 2 \pm \sqrt { 17 } i$

Question 13

Solve the equation by completing the square. $4 x ^ { 2 } - 5 x + 28 = 0$

Accepted Answer

A)  $x = \frac { 5 } { 8 } \pm \frac { \sqrt { 423 } i } { 8 }$ 
B)  $x = \frac { 25 } { 8 } \pm \frac { \sqrt { 62 } i } { 2 }$ 
C)  $x = \frac { 5 } { 8 } \pm \frac { \sqrt { 473 } } { 8 }$ 
D)  $x = \frac { 5 } { 8 } \pm \frac { \sqrt { 62 } } { 8 }$ 
E)  $x = \frac { 25 } { 8 } \pm \frac { \sqrt { 423 } } { 4 }$ 
A)  $x = \frac { 5 } { 8 } \pm \frac { \sqrt { 423 } i } { 8 }$ 
B)  $x = \frac { 25 } { 8 } \pm \frac { \sqrt { 62 } i } { 2 }$ 
C)  $x = \frac { 5 } { 8 } \pm \frac { \sqrt { 473 } } { 8 }$ 
D)  $x = \frac { 5 } { 8 } \pm \frac { \sqrt { 62 } } { 8 }$ 
E)  $x = \frac { 25 } { 8 } \pm \frac { \sqrt { 423 } } { 4 }$

Question 14

Solve the equation by completing the square. $y ^ { 2 } + 5 y + 12 = 0$

Accepted Answer

A)  $y = - \frac { 5 } { 2 } \pm$  $2 \sqrt { 3 }$ 
B)  $y = \frac { 5 } { 2 } \pm \frac { \sqrt { 23 } i } { 2 }$ 
C)  $y = - \frac { 5 } { 2 } \pm \frac { \sqrt { 23 } i } { 2 }$ 
D)  $y = \frac { 5 } { 2 } \pm \frac { \sqrt { 38 } i } { 2 }$ 
E)  $y = - \frac { 5 } { 2 } \pm \frac { \sqrt { 38 } i } { 2 }$ 
A)  $y = - \frac { 5 } { 2 } \pm$  $2 \sqrt { 3 }$ 
B)  $y = \frac { 5 } { 2 } \pm \frac { \sqrt { 23 } i } { 2 }$ 
C)  $y = - \frac { 5 } { 2 } \pm \frac { \sqrt { 23 } i } { 2 }$ 
D)  $y = \frac { 5 } { 2 } \pm \frac { \sqrt { 38 } i } { 2 }$ 
E)  $y = - \frac { 5 } { 2 } \pm \frac { \sqrt { 38 } i } { 2 }$

Question 15

Solve $25 ( y + 5 ) ^ { 2 } = 81$ by the Square Root Property, if possible.

Accepted Answer

A)  $y = - \frac { 16 } { 5 } , y = - \frac { 34 } { 5 }$ 
B)  $y = - \frac { 16 } { 5 } , y = \frac { 34 } { 5 }$ 
C)  $y = 4 , y = - 14$ 
D)  $y = \frac { 9 } { 5 } , y = - \frac { 9 } { 5 }$ 
E) no solutions 
A)  $y = - \frac { 16 } { 5 } , y = - \frac { 34 } { 5 }$ 
B)  $y = - \frac { 16 } { 5 } , y = \frac { 34 } { 5 }$ 
C)  $y = 4 , y = - 14$ 
D)  $y = \frac { 9 } { 5 } , y = - \frac { 9 } { 5 }$ 
E) no solutions

Question 16

If the area of a rectangle is 61.95 square meters, and the width is ten meters shorter than the length, find the perimeter of the rectangle in meters. Round your answer to two decimal places.

Accepted Answer

A)  35.49 meters 
B)  21.25 meters 
C)  61.95 meters 
D)  81.95 meters 
E)  41.95 meters 
A)  35.49 meters 
B)  21.25 meters 
C)  61.95 meters 
D)  81.95 meters 
E)  41.95 meters

Question 17

The height y (in feet)of a ball that you throw is given by $y = - \frac { 1 } { 180 } x ^ { 2 } + x + 6$ where x is the horizontal distance (in feet)from where you release the ball. How high is the ball when it reaches its maximum height?

Accepted Answer

A)  90  feet 
B)  51 feet 
C)  102 feet 
D)  6 feet 
E)  70 feet 
A)  90  feet 
B)  51 feet 
C)  102 feet 
D)  6 feet 
E)  70 feet

Question 18

Solve $5 z ^ { 2 } - 5 z - 4 = 0$  by completing the square. Round your answer to two decimal places.

Accepted Answer

A)  $x = - 1.52 , x = 0.52$ 
B)  $x = 1.12 , x = 0.52$ 
C)  $x = - 1.52 , x = 1.12$ 
D)  $x = 1.52 , x = - 0.52$ 
E)  $x = 5 , x = 4$ 
A)  $x = - 1.52 , x = 0.52$ 
B)  $x = 1.12 , x = 0.52$ 
C)  $x = - 1.52 , x = 1.12$ 
D)  $x = 1.52 , x = - 0.52$ 
E)  $x = 5 , x = 4$

Question 19

You have 200 meters of fencing to enclose two adjacent rectangular corrals. The total area of the enclosed region is 1000 square meters. What are the dimensions of each corral? (The corrals are the same size.)

Accepted Answer

A)  $\frac { 5 \sqrt { 1375 } } { 2 }$+25 meters by $\frac { 100 + 10 \sqrt { 1375 } } { 3 }$ maters 
B)  $\frac { 5 \sqrt { 1375 } } { 2 }$ +25 meters by $\frac { 100 - 10 \sqrt { 40 } } { 3 }$ maters 
C)  $\frac { 5 \sqrt { 1375 } } { 2 }$ +25 meters by $\frac { 100 + 10 \sqrt { 40 } } { 3 }$ maters 
D)  $\frac { 5 \sqrt { 40 } } { 2 }$ +25 meters by $\frac { 100 - 10 \sqrt { 40 } } { 3 }$ maters 
E)  $\frac { 5 \sqrt { 40 } } { 2 }$ +25 meters by $100 - \frac { 5 \sqrt { 40 } } { 2 }$ maters 
A)  $\frac { 5 \sqrt { 1375 } } { 2 }$+25 meters by $\frac { 100 + 10 \sqrt { 1375 } } { 3 }$ maters 
B)  $\frac { 5 \sqrt { 1375 } } { 2 }$ +25 meters by $\frac { 100 - 10 \sqrt { 40 } } { 3 }$ maters 
C)  $\frac { 5 \sqrt { 1375 } } { 2 }$ +25 meters by $\frac { 100 + 10 \sqrt { 40 } } { 3 }$ maters 
D)  $\frac { 5 \sqrt { 40 } } { 2 }$ +25 meters by $\frac { 100 - 10 \sqrt { 40 } } { 3 }$ maters 
E)  $\frac { 5 \sqrt { 40 } } { 2 }$ +25 meters by $100 - \frac { 5 \sqrt { 40 } } { 2 }$ maters

Question 20

The height h (in feet)of a falling object above the ground at time t (in seconds)is modeled by $h = h _ { 0 } - 16 t ^ { 2 }$ , where $h _ { 0 }$ is the initial height. Find the time (in seconds)it takes for an object to fall to the ground if the initial height is 630 feet. Round your answer to two decimal places.

Accepted Answer

A)  19.69 seconds 
B)  4.44 seconds 
C)  1.59 seconds 
D)  6.27 seconds 
E)  12.55 seconds 
A)  19.69 seconds 
B)  4.44 seconds 
C)  1.59 seconds 
D)  6.27 seconds 
E)  12.55 seconds

Sketch the graph of $h ( x ) = - ( x + 4 ) ^ { 2 }$ .

Solve $t ^ { 2 } + 7 t = 0$ by factoring.

Determine the intervals for which $4 x ( x - 5 )$ is entirely negative and entirely positive.

Determine the intervals for which $x ^ { 2 } - 4 x - 45$ is entirely negative and entirely positive.

Find the critical numbers. $\frac { 4 } { x - 3 }$

The height h (in feet)of an object dropped from a tower 54 feet high is modeled by $h = 54 - 16 t ^ { 2 }$ , where t is the time in seconds. How long does it take for the object to reach the ground? Round your answer to two decimal places.

Use a graphing calculator to solve the inequality $x ^ { 2 } + 12 x + 32 \geq 92$ . Round all numerical values in your answer to three decimal places, where applicable.

Solve the inequality $\frac { x - 1 } { x - 5 } \leq 3$ and graph the solution on the real number line.

Graph the solution to the inequality on the real line. $\frac { 4 } { x - 4 } > 0$

Find the intercepts of $y = 9 x ^ { 2 } - 8 x + 8$ .

What term should be added to $y ^ { 2 } - \frac { 1 } { 5 } y$ to make it a perfect square trinomial?

Solve the equation by using the Square Root Property. $( 2 x + 2 ) ^ { 2 } = - 17$

Solve the equation by completing the square. $4 x ^ { 2 } - 5 x + 28 = 0$

Solve the equation by completing the square. $y ^ { 2 } + 5 y + 12 = 0$

Solve $25 ( y + 5 ) ^ { 2 } = 81$ by the Square Root Property, if possible.

If the area of a rectangle is 61.95 square meters, and the width is ten meters shorter than the length, find the perimeter of the rectangle in meters. Round your answer to two decimal places.

The height y (in feet)of a ball that you throw is given by $y = - \frac { 1 } { 180 } x ^ { 2 } + x + 6$ where x is the horizontal distance (in feet)from where you release the ball. How high is the ball when it reaches its maximum height?

Solve $5 z ^ { 2 } - 5 z - 4 = 0$ by completing the square. Round your answer to two decimal places.

You have 200 meters of fencing to enclose two adjacent rectangular corrals. The total area of the enclosed region is 1000 square meters. What are the dimensions of each corral? (The corrals are the same size.)

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

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Rational Expressions, Equations, and Functions

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Exam 8: Quadratic Equations, Functions, and Inequalities

Sketch the graph of h(x)=−(x+4)2h ( x ) = - ( x + 4 ) ^ { 2 }h(x)=−(x+4)2 .

Solve t2+7t=0t ^ { 2 } + 7 t = 0t2+7t=0 by factoring.

Determine the intervals for which 4x(x−5)4 x ( x - 5 )4x(x−5) is entirely negative and entirely positive.

Determine the intervals for which x2−4x−45x ^ { 2 } - 4 x - 45x2−4x−45 is entirely negative and entirely positive.

Find the critical numbers. 4x−3\frac { 4 } { x - 3 }x−34​

The height h (in feet)of an object dropped from a tower 54 feet high is modeled by h=54−16t2h = 54 - 16 t ^ { 2 }h=54−16t2 , where t is the time in seconds. How long does it take for the object to reach the ground? Round your answer to two decimal places.

Use a graphing calculator to solve the inequality x2+12x+32≥92x ^ { 2 } + 12 x + 32 \geq 92x2+12x+32≥92 . Round all numerical values in your answer to three decimal places, where applicable.

Solve the inequality x−1x−5≤3\frac { x - 1 } { x - 5 } \leq 3x−5x−1​≤3 and graph the solution on the real number line.

Graph the solution to the inequality on the real line. 4x−4>0\frac { 4 } { x - 4 } > 0x−44​>0

Find the intercepts of y=9x2−8x+8y = 9 x ^ { 2 } - 8 x + 8y=9x2−8x+8 .

What term should be added to y2−15yy ^ { 2 } - \frac { 1 } { 5 } yy2−51​y to make it a perfect square trinomial?

Solve the equation by using the Square Root Property. (2x+2)2=−17( 2 x + 2 ) ^ { 2 } = - 17(2x+2)2=−17

Solve the equation by completing the square. 4x2−5x+28=04 x ^ { 2 } - 5 x + 28 = 04x2−5x+28=0

Solve the equation by completing the square. y2+5y+12=0y ^ { 2 } + 5 y + 12 = 0y2+5y+12=0

Solve 25(y+5)2=8125 ( y + 5 ) ^ { 2 } = 8125(y+5)2=81 by the Square Root Property, if possible.

If the area of a rectangle is 61.95 square meters, and the width is ten meters shorter than the length, find the perimeter of the rectangle in meters. Round your answer to two decimal places.

The height y (in feet)of a ball that you throw is given by y=−1180x2+x+6y = - \frac { 1 } { 180 } x ^ { 2 } + x + 6y=−1801​x2+x+6 where x is the horizontal distance (in feet)from where you release the ball. How high is the ball when it reaches its maximum height?

Solve 5z2−5z−4=05 z ^ { 2 } - 5 z - 4 = 05z2−5z−4=0 by completing the square. Round your answer to two decimal places.

You have 200 meters of fencing to enclose two adjacent rectangular corrals. The total area of the enclosed region is 1000 square meters. What are the dimensions of each corral? (The corrals are the same size.)

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

Sketch the graph of $h ( x ) = - ( x + 4 ) ^ { 2 }$ .

Solve $t ^ { 2 } + 7 t = 0$ by factoring.

Determine the intervals for which $4 x ( x - 5 )$ is entirely negative and entirely positive.

Determine the intervals for which $x ^ { 2 } - 4 x - 45$ is entirely negative and entirely positive.

Find the critical numbers. $\frac { 4 } { x - 3 }$

The height h (in feet)of an object dropped from a tower 54 feet high is modeled by $h = 54 - 16 t ^ { 2 }$ , where t is the time in seconds. How long does it take for the object to reach the ground? Round your answer to two decimal places.

Use a graphing calculator to solve the inequality $x ^ { 2 } + 12 x + 32 \geq 92$ . Round all numerical values in your answer to three decimal places, where applicable.

Solve the inequality $\frac { x - 1 } { x - 5 } \leq 3$ and graph the solution on the real number line.

Graph the solution to the inequality on the real line. $\frac { 4 } { x - 4 } > 0$

Find the intercepts of $y = 9 x ^ { 2 } - 8 x + 8$ .

What term should be added to $y ^ { 2 } - \frac { 1 } { 5 } y$ to make it a perfect square trinomial?

Solve the equation by using the Square Root Property. $( 2 x + 2 ) ^ { 2 } = - 17$

Solve the equation by completing the square. $4 x ^ { 2 } - 5 x + 28 = 0$

Solve the equation by completing the square. $y ^ { 2 } + 5 y + 12 = 0$

Solve $25 ( y + 5 ) ^ { 2 } = 81$ by the Square Root Property, if possible.

The height y (in feet)of a ball that you throw is given by $y = - \frac { 1 } { 180 } x ^ { 2 } + x + 6$ where x is the horizontal distance (in feet)from where you release the ball. How high is the ball when it reaches its maximum height?

Solve $5 z ^ { 2 } - 5 z - 4 = 0$ by completing the square. Round your answer to two decimal places.