Question 1

Solve $u ^ { 2 } - 7 u - 4 = 0$ by completing the square, if possible.

Accepted Answer

A)  $y = \frac { \sqrt { 65 } } { 2 } , y = - \frac { \sqrt { 65 } } { 2 }$ 
B)  $y = \frac { 7 } { 2 } + \frac { \sqrt { 65 } } { 2 } , y = \frac { 7 } { 2 } - \frac { \sqrt { 65 } } { 2 }$ 
C)  $y = 7 + \frac { \sqrt { 65 } } { 2 } , y = 7 - \frac { \sqrt { 65 } } { 2 }$ 
D)  $y = - \frac { 7 } { 2 } + \frac { \sqrt { 65 } } { 2 } , y = - \frac { 7 } { 2 } - \frac { \sqrt { 65 } } { 2 }$ 
E) no solutions 
A)  $y = \frac { \sqrt { 65 } } { 2 } , y = - \frac { \sqrt { 65 } } { 2 }$ 
B)  $y = \frac { 7 } { 2 } + \frac { \sqrt { 65 } } { 2 } , y = \frac { 7 } { 2 } - \frac { \sqrt { 65 } } { 2 }$ 
C)  $y = 7 + \frac { \sqrt { 65 } } { 2 } , y = 7 - \frac { \sqrt { 65 } } { 2 }$ 
D)  $y = - \frac { 7 } { 2 } + \frac { \sqrt { 65 } } { 2 } , y = - \frac { 7 } { 2 } - \frac { \sqrt { 65 } } { 2 }$ 
E) no solutions B

Question 2

Find the real solutions of the equation $\sqrt { 2 x + 114 } = x - 5$ .

Accepted Answer

A)  $6 - \sqrt { 5 }$ 
B)  $6 \pm 5 \sqrt { 5 }$ 
C)  $12 \pm 10 \sqrt { 5 }$ 
D)  $5 + 6 \sqrt { 5 }$ 
E)  $10 + \sqrt { 5 }$ 
A)  $6 - \sqrt { 5 }$ 
B)  $6 \pm 5 \sqrt { 5 }$ 
C)  $12 \pm 10 \sqrt { 5 }$ 
D)  $5 + 6 \sqrt { 5 }$ 
E)  $10 + \sqrt { 5 }$ B

Question 3

From the roof of a building 125 feet above the ground, you toss a coin upward with an initial velocity of 11 feet per second. The height h (in feet)of the coin at time t (in seconds)after it is tossed is modeled by $h = - 16 t ^ { 2 } + 11 t + 125$ . Find the time when the coin hits the ground. Round your answer to two decimal places

Accepted Answer

A) 2.47 seconds 
B) 50.56 seconds 
C) 3.16 seconds 
D) 39.56 seconds 
E) 6.51 seconds 
A) 2.47 seconds 
B) 50.56 seconds 
C) 3.16 seconds 
D) 39.56 seconds 
E) 6.51 seconds C

Question 4

A picture is 6 inches longer than it is wide and has an area of 167 square inches. What are the dimensions (in inches)of the picture. Round your answers to two decimal places.

Accepted Answer

A)  12.92 inches  × 18.92 inches 
B)  4.27 inches  × 10.27 inches 
C)  10.27 inches  × 16.27 inches 
D)  4.27 inches  × $16.27$ inches 
E)  $83.5$ inches  × $89.5$ inches 
A)  12.92 inches  × 18.92 inches 
B)  4.27 inches  × 10.27 inches 
C)  10.27 inches  × 16.27 inches 
D)  4.27 inches  × $16.27$ inches 
E)  $83.5$ inches  × $89.5$ inches

Question 5

Solve $u ( u - 10 ) - 6 ( u - 10 ) = 0$ by factoring.

Accepted Answer

A)  $u = 6 , u = 10$ 
B)  $u = 0 , u = \frac { 3 } { 5 }$ 
C)  $u = - 6 , u = - 10$ 
D)  $u = 0 , u = 10$ 
E)  $u = 6 , u = - 10$ 
A)  $u = 6 , u = 10$ 
B)  $u = 0 , u = \frac { 3 } { 5 }$ 
C)  $u = - 6 , u = - 10$ 
D)  $u = 0 , u = 10$ 
E)  $u = 6 , u = - 10$

Question 6

Determine if the parabola $y = - 2 x ^ { 2 } - 7 x + 8$ opens upward or downward.

Accepted Answer

A) parabola opens upward 
B) parabola opens downward 
A) parabola opens upward 
B) parabola opens downward

Question 7

Solve the equation by using the Quadratic Formula. $x ^ { 2 } - 8 x + 28 = 0$

Accepted Answer

A)  $x = - 32 \pm$  $2 i \sqrt { 3 }$ 
B)  $x = - 4 \pm$  $2 i \sqrt { 3 }$ 
C)  $x = - \frac { 4 } { 2 } \pm$ $2 i \sqrt { 3 }$ 
D)  $x = - \frac { 4 } { 2 } \pm$ $2 i \sqrt { 3 }$ 
E)  $x = 4 \pm$ $2 i \sqrt { 3 }$ 
A)  $x = - 32 \pm$  $2 i \sqrt { 3 }$ 
B)  $x = - 4 \pm$  $2 i \sqrt { 3 }$ 
C)  $x = - \frac { 4 } { 2 } \pm$ $2 i \sqrt { 3 }$ 
D)  $x = - \frac { 4 } { 2 } \pm$ $2 i \sqrt { 3 }$ 
E)  $x = 4 \pm$ $2 i \sqrt { 3 }$

Question 8

A rectangular playing field with a perimeter of $120$ meters is to have an area of at least $495$ square meters. Within what bounds must the length of the field lie?

Accepted Answer

A) between $30$ and $30 + 9 \sqrt { 5 }$ meters 
B) between $30 - 9 \sqrt { 5 }$ and $30 + 9 \sqrt { 5 }$ meters 
C) between $28 \frac { 1 } { 2 }$ and $30$ meters 
D) between $28 \frac { 1 } { 2 }$ and $30 + 9 \sqrt { 5 }$ meters 
E) between $28 \frac { 1 } { 2 }$ and $9$ meters 
A) between $30$ and $30 + 9 \sqrt { 5 }$ meters 
B) between $30 - 9 \sqrt { 5 }$ and $30 + 9 \sqrt { 5 }$ meters 
C) between $28 \frac { 1 } { 2 }$ and $30$ meters 
D) between $28 \frac { 1 } { 2 }$ and $30 + 9 \sqrt { 5 }$ meters 
E) between $28 \frac { 1 } { 2 }$ and $9$ meters

Question 9

Determine if the parabola $y = x ^ { 2 } - 5 x + 8$ opens upward or downward.

Accepted Answer

A) parabola opens downward 
B) parabola opens upward 
A) parabola opens downward 
B) parabola opens upward

Question 10

Use a graphing calculator to approximate the x -intercepts of the graph of the function $y = x ^ { 2 } + 2 x - 5$ . Round your answer to two decimal places wherever applicable.

Accepted Answer

A)  $( 5,0 ) , ( - 5,0 )$ 
B)  $( 0,3.45 ) , ( 0 , - 1.45 )$ 
C)  $( 0,1.45 ) , ( 0 , - 3.45 )$ 
D)  $( 1.45,0 ) , ( - 3.45,0 )$ 
E)  $( 3.45,0 ) , ( - 1.45,0 )$ 
A)  $( 5,0 ) , ( - 5,0 )$ 
B)  $( 0,3.45 ) , ( 0 , - 1.45 )$ 
C)  $( 0,1.45 ) , ( 0 , - 3.45 )$ 
D)  $( 1.45,0 ) , ( - 3.45,0 )$ 
E)  $( 3.45,0 ) , ( - 1.45,0 )$

Question 11

Use the Quadratic Formula to solve $\sqrt { 9 x + 5 } = x - 1$ , if possible. Round your answer(s)to two decimal places.

Accepted Answer

A)  $x = 22.70 , x = - 0.70$ 
B)  $x = - 11.35 , x = - 0.35$ 
C)  $x = 0.35 , x = - 6.62$ 
D)  $x = 11.35$ 
E) no solutions 
A)  $x = 22.70 , x = - 0.70$ 
B)  $x = - 11.35 , x = - 0.35$ 
C)  $x = 0.35 , x = - 6.62$ 
D)  $x = 11.35$ 
E) no solutions

Question 12

The product of two consecutive odd integers is 783 . Find two positive integers that satisfy this requirement.

Accepted Answer

A)  29 and 31 
B)  27 and 29 
C)  27 and 28 
D)  31 and 33 
E)  25 and 27 
A)  29 and 31 
B)  27 and 29 
C)  27 and 28 
D)  31 and 33 
E)  25 and 27

Question 13

Find two consecutive positive integers whose product is 462 .

Accepted Answer

A)  22,23 
B)  18,19 
C)  21,22 
D)  17,18 
E)  19,20 
A)  22,23 
B)  18,19 
C)  21,22 
D)  17,18 
E)  19,20

Question 14

Write an equation of the parabola $y = a ( x - h ) ^ { 2 } + k$ that satisfies the conditions. Vertex: (2,6) ; a=1

Accepted Answer

A)  $y = ( x + 2 ) ^ { 2 } + 6$ 
B)  $y = ( x + 6 ) ^ { 2 } + 2$ 
C)  $y = ( x - 6 ) ^ { 2 } + 2$ 
D)  $y = ( x - 2 ) ^ { 2 } + 6$ 
E)  $y = ( x + 2 ) ^ { 2 } - 6$ 
A)  $y = ( x + 2 ) ^ { 2 } + 6$ 
B)  $y = ( x + 6 ) ^ { 2 } + 2$ 
C)  $y = ( x - 6 ) ^ { 2 } + 2$ 
D)  $y = ( x - 2 ) ^ { 2 } + 6$ 
E)  $y = ( x + 2 ) ^ { 2 } - 6$

Question 15

Solve $\frac { x } { 3 } + \frac { 2 } { x } = 6$ . Round your answer to two decimal places.

Accepted Answer

A)  $x = - 17.66 , x = - 0.34$ 
B)  $x = 6.00 , x = 3.00$ 
C)  $x = - 17.66 , x = 0.71$ 
D)  $x = 17.66 , x = 0.34$ 
E)  $x = - 0.34 , x = 0.71$ 
A)  $x = - 17.66 , x = - 0.34$ 
B)  $x = 6.00 , x = 3.00$ 
C)  $x = - 17.66 , x = 0.71$ 
D)  $x = 17.66 , x = 0.34$ 
E)  $x = - 0.34 , x = 0.71$

Question 16

Write $x ^ { 2 } + 6 x = - 5$ in general form.

Accepted Answer

A)  $x ^ { 2 } + 11 x + 5 = 0$ 
B)  $x ^ { 2 } + 6 x + 5 = 0$ 
C)  $x ^ { 2 } + 6 x - 5 = 0$ 
D)  $x ^ { 2 } - 6 x + 5 = 0$ 
E)  $x ^ { 2 } = - 6 x - 5$ 
A)  $x ^ { 2 } + 11 x + 5 = 0$ 
B)  $x ^ { 2 } + 6 x + 5 = 0$ 
C)  $x ^ { 2 } + 6 x - 5 = 0$ 
D)  $x ^ { 2 } - 6 x + 5 = 0$ 
E)  $x ^ { 2 } = - 6 x - 5$

Question 17

The height y (in feet)of a ball that you throw is given by $y = - \frac { 1 } { 150 } x ^ { 2 } + x + 6$ where x is the horizontal distance (in feet)from where you release the ball. How far away does the ball strike the ground from where you release it? Round to the nearest foot.

Accepted Answer

A)  156 feet 
B)  75 feet 
C)  87 feet 
D)  6 feet 
E)  81 feet 
A)  156 feet 
B)  75 feet 
C)  87 feet 
D)  6 feet 
E)  81 feet

Question 18

Solve $( y - 5 ) ^ { 2 } = 144$ by the Square Root Property, if possible.

Accepted Answer

A)  $y = 12 , y = - 12$ 
B)  $y = 17 , y = - 7$ 
C)  y=139 
D)  $y = - 17 , y = - 7$ 
E) no solutions 
A)  $y = 12 , y = - 12$ 
B)  $y = 17 , y = - 7$ 
C)  y=139 
D)  $y = - 17 , y = - 7$ 
E) no solutions

Question 19

Graph the solution to the inequality $- 4 x ^ { 2 } + 8 x - 9 > - 13$ .

Accepted Answer

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

Question 20

Solve the equation by using the Quadratic Formula. $u ^ { 2 } - 10 u + 18 = 0$

Accepted Answer

A)  $u = 10 \pm$  $\sqrt { 7 }$ 
B)  $u = 10 \pm$ $\sqrt { 43 }$ 
C)  $u = 5 \pm$ $\sqrt { 7 }$ 
D)  $u = - 10 \pm$ $\sqrt { 43 }$ 
E)  $u = - 5 \pm$  $\sqrt { 7 }$ 
A)  $u = 10 \pm$  $\sqrt { 7 }$ 
B)  $u = 10 \pm$ $\sqrt { 43 }$ 
C)  $u = 5 \pm$ $\sqrt { 7 }$ 
D)  $u = - 10 \pm$ $\sqrt { 43 }$ 
E)  $u = - 5 \pm$  $\sqrt { 7 }$

Solve $u ^ { 2 } - 7 u - 4 = 0$ by completing the square, if possible.

Find the real solutions of the equation $\sqrt { 2 x + 114 } = x - 5$ .

A picture is 6 inches longer than it is wide and has an area of 167 square inches. What are the dimensions (in inches)of the picture. Round your answers to two decimal places.

Solve $u ( u - 10 ) - 6 ( u - 10 ) = 0$ by factoring.

Determine if the parabola $y = - 2 x ^ { 2 } - 7 x + 8$ opens upward or downward.

Solve the equation by using the Quadratic Formula. $x ^ { 2 } - 8 x + 28 = 0$

A rectangular playing field with a perimeter of $120$ meters is to have an area of at least $495$ square meters. Within what bounds must the length of the field lie?

Determine if the parabola $y = x ^ { 2 } - 5 x + 8$ opens upward or downward.

Use a graphing calculator to approximate the x -intercepts of the graph of the function $y = x ^ { 2 } + 2 x - 5$ . Round your answer to two decimal places wherever applicable.

Use the Quadratic Formula to solve $\sqrt { 9 x + 5 } = x - 1$ , if possible. Round your answer(s)to two decimal places.

The product of two consecutive odd integers is 783 . Find two positive integers that satisfy this requirement.

Find two consecutive positive integers whose product is 462 .

Write an equation of the parabola $y = a ( x - h ) ^ { 2 } + k$ that satisfies the conditions. Vertex: (2,6) ; a=1

Solve $\frac { x } { 3 } + \frac { 2 } { x } = 6$ . Round your answer to two decimal places.

Write $x ^ { 2 } + 6 x = - 5$ in general form.

The height y (in feet)of a ball that you throw is given by $y = - \frac { 1 } { 150 } x ^ { 2 } + x + 6$ where x is the horizontal distance (in feet)from where you release the ball. How far away does the ball strike the ground from where you release it? Round to the nearest foot.

Solve $( y - 5 ) ^ { 2 } = 144$ by the Square Root Property, if possible.

Graph the solution to the inequality $- 4 x ^ { 2 } + 8 x - 9 > - 13$ .

Solve the equation by using the Quadratic Formula. $u ^ { 2 } - 10 u + 18 = 0$

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

Solve u2−7u−4=0u ^ { 2 } - 7 u - 4 = 0u2−7u−4=0 by completing the square, if possible.

Find the real solutions of the equation 2x+114=x−5\sqrt { 2 x + 114 } = x - 52x+114​=x−5 .

A picture is 6 inches longer than it is wide and has an area of 167 square inches. What are the dimensions (in inches)of the picture. Round your answers to two decimal places.

Solve u(u−10)−6(u−10)=0u ( u - 10 ) - 6 ( u - 10 ) = 0u(u−10)−6(u−10)=0 by factoring.

Determine if the parabola y=−2x2−7x+8y = - 2 x ^ { 2 } - 7 x + 8y=−2x2−7x+8 opens upward or downward.

Solve the equation by using the Quadratic Formula. x2−8x+28=0x ^ { 2 } - 8 x + 28 = 0x2−8x+28=0

A rectangular playing field with a perimeter of 120120120 meters is to have an area of at least 495495495 square meters. Within what bounds must the length of the field lie?

Determine if the parabola y=x2−5x+8y = x ^ { 2 } - 5 x + 8y=x2−5x+8 opens upward or downward.

Use a graphing calculator to approximate the x -intercepts of the graph of the function y=x2+2x−5y = x ^ { 2 } + 2 x - 5y=x2+2x−5 . Round your answer to two decimal places wherever applicable.

Use the Quadratic Formula to solve 9x+5=x−1\sqrt { 9 x + 5 } = x - 19x+5​=x−1 , if possible. Round your answer(s)to two decimal places.

The product of two consecutive odd integers is 783 . Find two positive integers that satisfy this requirement.

Find two consecutive positive integers whose product is 462 .

Write an equation of the parabola y=a(x−h)2+ky = a ( x - h ) ^ { 2 } + ky=a(x−h)2+k that satisfies the conditions. Vertex: (2,6) ; a=1

Solve x3+2x=6\frac { x } { 3 } + \frac { 2 } { x } = 63x​+x2​=6 . Round your answer to two decimal places.

Write x2+6x=−5x ^ { 2 } + 6 x = - 5x2+6x=−5 in general form.

Solve (y−5)2=144( y - 5 ) ^ { 2 } = 144(y−5)2=144 by the Square Root Property, if possible.

Graph the solution to the inequality −4x2+8x−9>−13- 4 x ^ { 2 } + 8 x - 9 > - 13−4x2+8x−9>−13 .

Solve the equation by using the Quadratic Formula. u2−10u+18=0u ^ { 2 } - 10 u + 18 = 0u2−10u+18=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

Solve $u ^ { 2 } - 7 u - 4 = 0$ by completing the square, if possible.

Find the real solutions of the equation $\sqrt { 2 x + 114 } = x - 5$ .

Solve $u ( u - 10 ) - 6 ( u - 10 ) = 0$ by factoring.

Determine if the parabola $y = - 2 x ^ { 2 } - 7 x + 8$ opens upward or downward.

Solve the equation by using the Quadratic Formula. $x ^ { 2 } - 8 x + 28 = 0$

A rectangular playing field with a perimeter of $120$ meters is to have an area of at least $495$ square meters. Within what bounds must the length of the field lie?

Determine if the parabola $y = x ^ { 2 } - 5 x + 8$ opens upward or downward.

Use a graphing calculator to approximate the x -intercepts of the graph of the function $y = x ^ { 2 } + 2 x - 5$ . Round your answer to two decimal places wherever applicable.

Use the Quadratic Formula to solve $\sqrt { 9 x + 5 } = x - 1$ , if possible. Round your answer(s)to two decimal places.

Write an equation of the parabola $y = a ( x - h ) ^ { 2 } + k$ that satisfies the conditions. Vertex: (2,6) ; a=1

Solve $\frac { x } { 3 } + \frac { 2 } { x } = 6$ . Round your answer to two decimal places.

Write $x ^ { 2 } + 6 x = - 5$ in general form.

Solve $( y - 5 ) ^ { 2 } = 144$ by the Square Root Property, if possible.

Graph the solution to the inequality $- 4 x ^ { 2 } + 8 x - 9 > - 13$ .

Solve the equation by using the Quadratic Formula. $u ^ { 2 } - 10 u + 18 = 0$