Question 1

Graph the solution to the inequality on the real line. $\frac { 1 } { x + 3 } \geq - 4$

Accepted Answer

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

Question 2

Solve the equation of quadratic form. $\frac { 1 } { x ^ { 2 } } - \frac { 3 } { x } - 18 = 0$

Accepted Answer

A)  $x = \frac { 1 } { 3 } ; x = - \frac { 1 } { 6 }$ 
B)  $x = - \frac { 1 } { 3 } ; x = \frac { 1 } { 6 }$ 
C)  $x = 3 ; x = - 6$ 
D)  $x = 9 ; x = 36$ 
E)  $x = - 3 ; x = 6$ 
A)  $x = \frac { 1 } { 3 } ; x = - \frac { 1 } { 6 }$ 
B)  $x = - \frac { 1 } { 3 } ; x = \frac { 1 } { 6 }$ 
C)  $x = 3 ; x = - 6$ 
D)  $x = 9 ; x = 36$ 
E)  $x = - 3 ; x = 6$

Question 3

Find the vertex of  $y = 5 - 3 x - x ^ { 2 }$ .

Accepted Answer

A)  $\left( - \frac { 3 } { 2 } , \frac { 4 } { 29 } \right)$ 
B)  $\left( \frac { 2 } { 3 } , \frac { 4 } { 29 } \right)$ 
C)  $\left( - \frac { 3 } { 2 } , \frac { 29 } { 4 } \right)$ 
D)  $\left( \frac { 3 } { 2 } , \frac { 29 } { 4 } \right)$ 
E)  $\left( - 3 , \frac { 29 } { 4 } \right)$ 
A)  $\left( - \frac { 3 } { 2 } , \frac { 4 } { 29 } \right)$ 
B)  $\left( \frac { 2 } { 3 } , \frac { 4 } { 29 } \right)$ 
C)  $\left( - \frac { 3 } { 2 } , \frac { 29 } { 4 } \right)$ 
D)  $\left( \frac { 3 } { 2 } , \frac { 29 } { 4 } \right)$ 
E)  $\left( - 3 , \frac { 29 } { 4 } \right)$

Question 4

Solve the equation by completing the square. Round your solution to two decimal places. $0.1 x ^ { 2 } + 0.5 x = 0.7$

Accepted Answer

A)  $x = 6.14 , x = - 1.14$ 
B)  $x = - 5.58 , x = 0.58$ 
C)  $x = 1.14 , x = - 6.14$ 
D)  $x = - 0.13 \pm 3 i$ 
E)  $x = 0.13 \pm 3 i$ 
A)  $x = 6.14 , x = - 1.14$ 
B)  $x = - 5.58 , x = 0.58$ 
C)  $x = 1.14 , x = - 6.14$ 
D)  $x = - 0.13 \pm 3 i$ 
E)  $x = 0.13 \pm 3 i$

Question 5

Use a graphing calculator to determine the number of real solutions of the quadratic equation $4 x ^ { 2 } - 3 x + 9 = 0$ .

Accepted Answer

A) one real solution 
B) no real solutions 
C) two real solutions 
A) one real solution 
B) no real solutions 
C) two real solutions

Question 6

Use the Quadratic Formula to solve $4 x ^ { 2 } - 12 x + 6 = 0$ , if possible. Round your answer(s)to two decimal places.

Accepted Answer

A)  $x = 18.87 , x = 17.13$ 
B)  $x = - 0.63 , x = - 2.37$ 
C)  $x = 9.46 , x = 2.54$ 
D)  $x = 2.37 , x = 0.63$ 
E) no solutions 
A)  $x = 18.87 , x = 17.13$ 
B)  $x = - 0.63 , x = - 2.37$ 
C)  $x = 9.46 , x = 2.54$ 
D)  $x = 2.37 , x = 0.63$ 
E) no solutions

Question 7

From the roof of a building 100 feet above the ground, you toss a coin upward with an initial velocity of 6 feet per second. The height h (in feet)of the coin at time t (in seconds)after it is tossed is modeled by $h = - 16 t ^ { 2 } + 6 t + 100$ . Find the time when the coin is again 100 feet above the ground.

Accepted Answer

A)  $\frac { 3 } { 8 }$ second 
B) 0 second 
C)  $\frac { 3 } { 16 }$ second 
D)  $\frac { 3 } { 4 }$ second 
E)  $\frac { 8 } { 3 }$ seconds 
A)  $\frac { 3 } { 8 }$ second 
B) 0 second 
C)  $\frac { 3 } { 16 }$ second 
D)  $\frac { 3 } { 4 }$ second 
E)  $\frac { 8 } { 3 }$ seconds

Question 8

Solve the equation $x \left( x - \frac { 2 } { 3 } \right) = 14$ by completing the square. Give the solutions in exact form and in decimal form rounded to two decimal places. (The solutions may be complex numbers.)

Accepted Answer

A)  $- \frac { 1 } { 3 } + \frac { \sqrt { 127 } } { 6 } \approx 1.54 ; - \frac { 1 } { 3 } - \frac { \sqrt { 127 } } { 6 } \approx - 2.21$ 
B)  $\frac { 2 } { 3 } + \frac { \sqrt { 127 } } { 3 } \approx 4.42 ; \frac { 2 } { 3 } - \frac { \sqrt { 127 } } { 3 } \approx - 3.09$ 
C)  $\frac { 1 } { 3 } + \frac { \sqrt { 127 } } { 3 } \approx 4.09 ; \frac { 1 } { 3 } - \frac { \sqrt { 127 } } { 3 } \approx - 3.42$ 
D)  $\frac { 2 } { 3 } + \frac { \sqrt { 127 } } { 6 } \approx 2.54 ; \frac { 2 } { 3 } - \frac { \sqrt { 127 } } { 6 } \approx - 1.21$ 
E)  $- \frac { 1 } { 3 } + \frac { \sqrt { 127 } } { 3 } \approx 3.42 ; - \frac { 2 } { 3 } - \frac { \sqrt { 127 } } { 3 } \approx - 4.42$ 
A)  $- \frac { 1 } { 3 } + \frac { \sqrt { 127 } } { 6 } \approx 1.54 ; - \frac { 1 } { 3 } - \frac { \sqrt { 127 } } { 6 } \approx - 2.21$ 
B)  $\frac { 2 } { 3 } + \frac { \sqrt { 127 } } { 3 } \approx 4.42 ; \frac { 2 } { 3 } - \frac { \sqrt { 127 } } { 3 } \approx - 3.09$ 
C)  $\frac { 1 } { 3 } + \frac { \sqrt { 127 } } { 3 } \approx 4.09 ; \frac { 1 } { 3 } - \frac { \sqrt { 127 } } { 3 } \approx - 3.42$ 
D)  $\frac { 2 } { 3 } + \frac { \sqrt { 127 } } { 6 } \approx 2.54 ; \frac { 2 } { 3 } - \frac { \sqrt { 127 } } { 6 } \approx - 1.21$ 
E)  $- \frac { 1 } { 3 } + \frac { \sqrt { 127 } } { 3 } \approx 3.42 ; - \frac { 2 } { 3 } - \frac { \sqrt { 127 } } { 3 } \approx - 4.42$

Question 9

Solve $x ^ { 2 } - 8 x - 9 = 0$ by completing the square, if possible.

Accepted Answer

A)  $x = - 1 , x = 9$ 
B)  $x = 8 , x = - 9$ 
C)  $x = 1 , x = - 9$ 
D)  $x = - 8 , x = - 9$ 
E) no solutions 
A)  $x = - 1 , x = 9$ 
B)  $x = 8 , x = - 9$ 
C)  $x = 1 , x = - 9$ 
D)  $x = - 8 , x = - 9$ 
E) no solutions

Question 10

Solve $u ^ { 2 } - 16 u = 0$ by completing the square.

Accepted Answer

A)  $u = - 16$ 
B)  $u = 0 , u = - 16$ 
C)  $u = 0 , u = 16$ 
D)  $u = 1 , u = 16$ 
E)  $u = 80 , u = - 48$ 
A)  $u = - 16$ 
B)  $u = 0 , u = - 16$ 
C)  $u = 0 , u = 16$ 
D)  $u = 1 , u = 16$ 
E)  $u = 80 , u = - 48$

Question 11

Solve $h ^ { 2 } = 100$ by the Square Root Property, if possible.

Accepted Answer

A)  $h = 10 , h = - 10$ 
B)  h=20 
C)  h=10 
D)  $h = 0 , h = 10$ 
E) no solutions 
A)  $h = 10 , h = - 10$ 
B)  h=20 
C)  h=10 
D)  $h = 0 , h = 10$ 
E) no solutions

Question 12

Solve the quadratic equation. $x ^ { 2 } + 6 x + 25 = 0$

Accepted Answer

A)  $x = 14 , x = - 2$ 
B)  $x = 1 , x = - 7$ 
C)  $x = - 6 \pm 8 i$ 
D)  $x = 6 \pm 8 i$ 
E)  $x = - 3 \pm 4 i$ 
A)  $x = 14 , x = - 2$ 
B)  $x = 1 , x = - 7$ 
C)  $x = - 6 \pm 8 i$ 
D)  $x = 6 \pm 8 i$ 
E)  $x = - 3 \pm 4 i$

Question 13

Use the Quadratic Formula to solve $t ^ { 2 } + 5 t + 6 = 0$ .

Accepted Answer

A)  $t = 2 , t = 3$ 
B)  $t = - 2 , t = 3$ 
C)  $t = 2 , t = - 3$ 
D)  $t = - 2 , t = - 3$ 
E) no solutions 
A)  $t = 2 , t = 3$ 
B)  $t = - 2 , t = 3$ 
C)  $t = 2 , t = - 3$ 
D)  $t = - 2 , t = - 3$ 
E) no solutions

Question 14

Find the critical numbers of $x ^ { 2 } - 7 x + 10$ .

Accepted Answer

A)  $- 2 , - 5$ 
B)  $0,5$ 
C)  $2,5$ 
D)  $2 , - 5$ 
E)  $0,2$ 
A)  $- 2 , - 5$ 
B)  $0,5$ 
C)  $2,5$ 
D)  $2 , - 5$ 
E)  $0,2$

Question 15

A rectangular corner lot has sidewalks on two adjacent sides for a total length of 85 feet. If the diagonal path across the lot is 64 feet, what are the length of the two sides of the walk? Round your answers to two decimal places.

Accepted Answer

A)  77.4 feet, 68.4 feet 
B)  42.5 feet, 42.5 feet 
C)  58.05 feet, 26.95 feet 
D)  80.12 feet, 70.12 feet 
E)  58.05 feet, 55.98 feet 
A)  77.4 feet, 68.4 feet 
B)  42.5 feet, 42.5 feet 
C)  58.05 feet, 26.95 feet 
D)  80.12 feet, 70.12 feet 
E)  58.05 feet, 55.98 feet

Question 16

After two years, a $1000 investment, compounded annually at interest rate r , will yield an amount of $1000 ( 1 + r ) ^ { 2 }$ . If the amount after two years is $1166.40, find the rate r . Round your answer to three decimal places.

Accepted Answer

A)  $r = 2.080$ 
B)  $r = 0.080$ 
C)  $r = 0.166$ 
D)  $r = 1.080$ 
E)  $r = 1.166$ 
A)  $r = 2.080$ 
B)  $r = 0.080$ 
C)  $r = 0.166$ 
D)  $r = 1.080$ 
E)  $r = 1.166$

Question 17

What term should be added to $y ^ { 2 } - 14 y$ to make it a perfect square trinomial?

Accepted Answer

A)  196 
B)  49 
C) 1 
D)  7 
E)  14 
A)  196 
B)  49 
C) 1 
D)  7 
E)  14

Question 18

Graph $y = x ^ { 2 } - 3 x$ .

Accepted Answer

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

Question 19

Solve the equation $( 4 m - 5 ) ^ { 2 } - 200 = 0$ by using the Square Root Property.

Accepted Answer

A)  $- \frac { 5 } { 4 } \pm \frac { 5 \sqrt { 2 } } { 4 }$ 
B)  $- \frac { 5 } { 2 } \pm \frac { 5 \sqrt { 2 } } { 4 }$ 
C)  $\frac { 5 } { 2 } \pm \frac { \sqrt { 2 } } { 2 }$ 
D)  $\frac { 5 } { 4 } \pm \frac { 5 \sqrt { 2 } } { 2 }$ 
E)  $\frac { 5 } { 4 } \pm \frac { \sqrt { 2 } } { 2 }$ 
A)  $- \frac { 5 } { 4 } \pm \frac { 5 \sqrt { 2 } } { 4 }$ 
B)  $- \frac { 5 } { 2 } \pm \frac { 5 \sqrt { 2 } } { 4 }$ 
C)  $\frac { 5 } { 2 } \pm \frac { \sqrt { 2 } } { 2 }$ 
D)  $\frac { 5 } { 4 } \pm \frac { 5 \sqrt { 2 } } { 2 }$ 
E)  $\frac { 5 } { 4 } \pm \frac { \sqrt { 2 } } { 2 }$

Question 20

An open box with a rectangular base of x inches by x+4 inches has a height of 6 inches. The volume of the box is 702 cubic inches. Find the dimensions of the box.

Accepted Answer

A)  11 inches by 15 inches by 6 inches 
B)  9 inches by 13 inches by 6 inches 
C)  15 inches by 19 inches by 6 inches 
D)  13 inches by $17$ inches by 6 inches 
E)  $13$ inches by $15$ inches by 6 inches 
A)  11 inches by 15 inches by 6 inches 
B)  9 inches by 13 inches by 6 inches 
C)  15 inches by 19 inches by 6 inches 
D)  13 inches by $17$ inches by 6 inches 
E)  $13$ inches by $15$ inches by 6 inches

Graph the solution to the inequality on the real line. $\frac { 1 } { x + 3 } \geq - 4$

Solve the equation of quadratic form. $\frac { 1 } { x ^ { 2 } } - \frac { 3 } { x } - 18 = 0$

Find the vertex of $y = 5 - 3 x - x ^ { 2 }$ .

Solve the equation by completing the square. Round your solution to two decimal places. $0.1 x ^ { 2 } + 0.5 x = 0.7$

Use a graphing calculator to determine the number of real solutions of the quadratic equation $4 x ^ { 2 } - 3 x + 9 = 0$ .

Use the Quadratic Formula to solve $4 x ^ { 2 } - 12 x + 6 = 0$ , if possible. Round your answer(s)to two decimal places.

Solve the equation $x \left( x - \frac { 2 } { 3 } \right) = 14$ by completing the square. Give the solutions in exact form and in decimal form rounded to two decimal places. (The solutions may be complex numbers.)

Solve $x ^ { 2 } - 8 x - 9 = 0$ by completing the square, if possible.

Solve $u ^ { 2 } - 16 u = 0$ by completing the square.

Solve $h ^ { 2 } = 100$ by the Square Root Property, if possible.

Solve the quadratic equation. $x ^ { 2 } + 6 x + 25 = 0$

Use the Quadratic Formula to solve $t ^ { 2 } + 5 t + 6 = 0$ .

Find the critical numbers of $x ^ { 2 } - 7 x + 10$ .

A rectangular corner lot has sidewalks on two adjacent sides for a total length of 85 feet. If the diagonal path across the lot is 64 feet, what are the length of the two sides of the walk? Round your answers to two decimal places.

After two years, a $1000 investment, compounded annually at interest rate r , will yield an amount of $1000 ( 1 + r ) ^ { 2 }$ . If the amount after two years is $1166.40, find the rate r . Round your answer to three decimal places.

What term should be added to $y ^ { 2 } - 14 y$ to make it a perfect square trinomial?

Graph $y = x ^ { 2 } - 3 x$ .

Solve the equation $( 4 m - 5 ) ^ { 2 } - 200 = 0$ by using the Square Root Property.

An open box with a rectangular base of x inches by x+4 inches has a height of 6 inches. The volume of the box is 702 cubic inches. Find the dimensions of the box.

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 line. 1x+3≥−4\frac { 1 } { x + 3 } \geq - 4x+31​≥−4

Solve the equation of quadratic form. 1x2−3x−18=0\frac { 1 } { x ^ { 2 } } - \frac { 3 } { x } - 18 = 0x21​−x3​−18=0

Find the vertex of y=5−3x−x2y = 5 - 3 x - x ^ { 2 }y=5−3x−x2 .

Solve the equation by completing the square. Round your solution to two decimal places. 0.1x2+0.5x=0.70.1 x ^ { 2 } + 0.5 x = 0.70.1x2+0.5x=0.7

Use a graphing calculator to determine the number of real solutions of the quadratic equation 4x2−3x+9=04 x ^ { 2 } - 3 x + 9 = 04x2−3x+9=0 .

Use the Quadratic Formula to solve 4x2−12x+6=04 x ^ { 2 } - 12 x + 6 = 04x2−12x+6=0 , if possible. Round your answer(s)to two decimal places.

Solve the equation x(x−23)=14x \left( x - \frac { 2 } { 3 } \right) = 14x(x−32​)=14 by completing the square. Give the solutions in exact form and in decimal form rounded to two decimal places. (The solutions may be complex numbers.)

Solve x2−8x−9=0x ^ { 2 } - 8 x - 9 = 0x2−8x−9=0 by completing the square, if possible.

Solve u2−16u=0u ^ { 2 } - 16 u = 0u2−16u=0 by completing the square.

Solve h2=100h ^ { 2 } = 100h2=100 by the Square Root Property, if possible.

Solve the quadratic equation. x2+6x+25=0x ^ { 2 } + 6 x + 25 = 0x2+6x+25=0

Use the Quadratic Formula to solve t2+5t+6=0t ^ { 2 } + 5 t + 6 = 0t2+5t+6=0 .

Find the critical numbers of x2−7x+10x ^ { 2 } - 7 x + 10x2−7x+10 .

A rectangular corner lot has sidewalks on two adjacent sides for a total length of 85 feet. If the diagonal path across the lot is 64 feet, what are the length of the two sides of the walk? Round your answers to two decimal places.

After two years, a $1000 investment, compounded annually at interest rate r , will yield an amount of 1000(1+r)21000 ( 1 + r ) ^ { 2 }1000(1+r)2 . If the amount after two years is $1166.40, find the rate r . Round your answer to three decimal places.

What term should be added to y2−14yy ^ { 2 } - 14 yy2−14y to make it a perfect square trinomial?

Graph y=x2−3xy = x ^ { 2 } - 3 xy=x2−3x .

Solve the equation (4m−5)2−200=0( 4 m - 5 ) ^ { 2 } - 200 = 0(4m−5)2−200=0 by using the Square Root Property.

An open box with a rectangular base of x inches by x+4 inches has a height of 6 inches. The volume of the box is 702 cubic inches. Find the dimensions of the box.

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 line. $\frac { 1 } { x + 3 } \geq - 4$

Solve the equation of quadratic form. $\frac { 1 } { x ^ { 2 } } - \frac { 3 } { x } - 18 = 0$

Find the vertex of $y = 5 - 3 x - x ^ { 2 }$ .

Solve the equation by completing the square. Round your solution to two decimal places. $0.1 x ^ { 2 } + 0.5 x = 0.7$

Use a graphing calculator to determine the number of real solutions of the quadratic equation $4 x ^ { 2 } - 3 x + 9 = 0$ .

Use the Quadratic Formula to solve $4 x ^ { 2 } - 12 x + 6 = 0$ , if possible. Round your answer(s)to two decimal places.

Solve the equation $x \left( x - \frac { 2 } { 3 } \right) = 14$ by completing the square. Give the solutions in exact form and in decimal form rounded to two decimal places. (The solutions may be complex numbers.)

Solve $x ^ { 2 } - 8 x - 9 = 0$ by completing the square, if possible.

Solve $u ^ { 2 } - 16 u = 0$ by completing the square.

Solve $h ^ { 2 } = 100$ by the Square Root Property, if possible.

Solve the quadratic equation. $x ^ { 2 } + 6 x + 25 = 0$

Use the Quadratic Formula to solve $t ^ { 2 } + 5 t + 6 = 0$ .

Find the critical numbers of $x ^ { 2 } - 7 x + 10$ .

After two years, a $1000 investment, compounded annually at interest rate r , will yield an amount of $1000 ( 1 + r ) ^ { 2 }$ . If the amount after two years is $1166.40, find the rate r . Round your answer to three decimal places.

What term should be added to $y ^ { 2 } - 14 y$ to make it a perfect square trinomial?

Graph $y = x ^ { 2 } - 3 x$ .

Solve the equation $( 4 m - 5 ) ^ { 2 } - 200 = 0$ by using the Square Root Property.