Question 1

Use a graphing calculator to determine the number of real solutions of the quadratic equation $7 x ^ { 2 } - 6 x - 6 = 0$ .

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 2

Use a graphing calculator to approximate the values of x that satisfy the inequality $- 5 x ^ { 2 } + 45 x - 9 > - 14$ . Round all numerical values in your answer to three decimal places, where applicable.

Accepted Answer

A)  $( - 0.717,9.717 )$ 
B)  $( - 0.11,9.11 )$ 
C)  $( 0 , \infty )$ 
D)  $( 0,9.11 )$ 
E)  $( - \infty , \infty )$ 
A)  $( - 0.717,9.717 )$ 
B)  $( - 0.11,9.11 )$ 
C)  $( 0 , \infty )$ 
D)  $( 0,9.11 )$ 
E)  $( - \infty , \infty )$

Question 3

Use the discriminant to determine the number of real solutions of $x ^ { 2 } - 2 x + 7 = 0$ .

Accepted Answer

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

Question 4

Solve the inequality $x ^ { 2 } + 2 x + 1 \geq 0$ and graph the solution on the real number line. (The inequality may have no solution.)

Accepted Answer

A) Solution: $( - 1 , \infty )$   
B) Solution: $( - \infty , \infty )$   
C) Solution: $( 1 , \infty )$   
D) Solution: $( - \infty , - 1 ) \cup ( 1 , \infty )$   
E) no solution 
A) Solution: $( - 1 , \infty )$   
B) Solution: $( - \infty , \infty )$   
C) Solution: $( 1 , \infty )$   
D) Solution: $( - \infty , - 1 ) \cup ( 1 , \infty )$   
E) no solution

Question 5

Graph the solution to the inequality $x ^ { 2 } - 3 x + 3 \leq 7$ .

Accepted Answer

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

Question 6

A projectile is fired straight upward from the ground level with an initial velocity of $112$ feet per second, so that its height h at any time t is given by $h = - 16 t ^ { 2 } + 112 t$ , where h is measured in feet and t is measured in seconds. During what interval(s)of time with the height of the projectile exceed $160$ feet?

Accepted Answer

A)  $( 2,5 )$ 
B)  $( 2,7 )$ 
C)  $( 5,7 )$ 
D)  $( 0,2 ) , ( 5,7 )$ 
E)  $( 1,7 )$ 
A)  $( 2,5 )$ 
B)  $( 2,7 )$ 
C)  $( 5,7 )$ 
D)  $( 0,2 ) , ( 5,7 )$ 
E)  $( 1,7 )$

Question 7

Use the Quadratic Formula to solve $12 x ^ { 2 } - 12 x + 3 = 0$ .

Accepted Answer

A)  $x = \frac { 1 } { 2 }$ 
B)  $x = \frac { 1 } { 2 } \pm 12 \sqrt { 2 }$ 
C)  $x = 12 \sqrt { 2 }$ 
D)  $x = - \frac { 1 } { 2 }$ 
E) no solutions 
A)  $x = \frac { 1 } { 2 }$ 
B)  $x = \frac { 1 } { 2 } \pm 12 \sqrt { 2 }$ 
C)  $x = 12 \sqrt { 2 }$ 
D)  $x = - \frac { 1 } { 2 }$ 
E) no solutions

Question 8

Graph the solution to the inequality on the real number line. $x ^ { 2 } + 3 x \geq 0$

Accepted Answer

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

Question 9

Solve the equation $x ^ { 2 } - 4 x - 3 = 0$ 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)  $4 + \sqrt { 7 } i \approx 4 + 2.65 i$ ; $4 - \sqrt { 7 } i \approx 4 - 2.65 i$ 
B)  $2 + \sqrt { 7 } i \approx 2 + 2.65 i$ ; $2 - \sqrt { 7 } i \approx 2 - 2.65 i$ 
C)  $4 + \sqrt { 7 } \approx 6.65$ ; $4 - \sqrt { 7 } \approx 1.35$ 
D)  $2 + \sqrt { 7 } \approx 4.65$ ; $2 - \sqrt { 7 } \approx - 0.65$ 
E)  $- 2 + \sqrt { 7 } \approx 0.65$ ; $- 2 - \sqrt { 7 } \approx - 4.65$ 
A)  $4 + \sqrt { 7 } i \approx 4 + 2.65 i$ ; $4 - \sqrt { 7 } i \approx 4 - 2.65 i$ 
B)  $2 + \sqrt { 7 } i \approx 2 + 2.65 i$ ; $2 - \sqrt { 7 } i \approx 2 - 2.65 i$ 
C)  $4 + \sqrt { 7 } \approx 6.65$ ; $4 - \sqrt { 7 } \approx 1.35$ 
D)  $2 + \sqrt { 7 } \approx 4.65$ ; $2 - \sqrt { 7 } \approx - 0.65$ 
E)  $- 2 + \sqrt { 7 } \approx 0.65$ ; $- 2 - \sqrt { 7 } \approx - 4.65$

Question 10

Use a graphing calculator to solve the rational inequality $x + \frac { 3 } { x } > 4$ . Round all numerical values in your answer to three decimal places, where applicable.

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( 1 , \infty )$ 
C)  $( 0,1 ) \cup ( 3 , \infty )$ 
D)  $( - \infty , - 1 ) \cup ( 3 , \infty )$ 
E)  $( - \infty , 1 ) \cup ( 3 , \infty )$ 
A)  $( - \infty , \infty )$ 
B)  $( 1 , \infty )$ 
C)  $( 0,1 ) \cup ( 3 , \infty )$ 
D)  $( - \infty , - 1 ) \cup ( 3 , \infty )$ 
E)  $( - \infty , 1 ) \cup ( 3 , \infty )$

Question 11

Solve the equation of quadratic form. $x - 4 \sqrt { x } - 12 = 0$

Accepted Answer

A)  $x = - 4 ; x = 36$ 
B)  $x = - 2 ; x = 6$ 
C)  x=36 
D)  $x = 2 ; x = - 6$ 
E)  $x = \sqrt { 2 } i ; x = \sqrt { 6 }$ 
A)  $x = - 4 ; x = 36$ 
B)  $x = - 2 ; x = 6$ 
C)  x=36 
D)  $x = 2 ; x = - 6$ 
E)  $x = \sqrt { 2 } i ; x = \sqrt { 6 }$

Question 12

Graph $y = - \left( x ^ { 2 } - 2 x - 6 \right)$ .

Accepted Answer

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

Question 13

Use the discriminant to determine the number of real solutions of $18 x ^ { 2 } - 12 x + 2 = 0$ .

Accepted Answer

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

Question 14

Find all real and complex solutions of the quadratic equation $( p - 3 ) ^ { 2 } - 243 = 0$ .

Accepted Answer

A)  $- 9 \pm 3 \sqrt { 3 }$ 
B)  $- 3 \pm 3 \sqrt { 3 } i$ 
C)  $- 3 \pm 9 \sqrt { 3 } i$ 
D)  $9 \pm 3 \sqrt { 3 }$ 
E)  $3 \pm 9 \sqrt { 3 }$ 
A)  $- 9 \pm 3 \sqrt { 3 }$ 
B)  $- 3 \pm 3 \sqrt { 3 } i$ 
C)  $- 3 \pm 9 \sqrt { 3 } i$ 
D)  $9 \pm 3 \sqrt { 3 }$ 
E)  $3 \pm 9 \sqrt { 3 }$

Question 15

Solve the equation $x ^ { 4 } - 37 x ^ { 2 } + 36 = 0$ . (Find all real and complex solutions.)

Accepted Answer

A)  $\pm 1 , \pm 6 i$ 
B)  $\pm 36$ 
C)  $\pm 1 , \pm 36$ 
D)  $\pm 1 , \pm 6$ 
E)  $\pm 6 i$ 
A)  $\pm 1 , \pm 6 i$ 
B)  $\pm 36$ 
C)  $\pm 1 , \pm 36$ 
D)  $\pm 1 , \pm 6$ 
E)  $\pm 6 i$

Question 16

Working together, two people can complete a task in 4.5 hours. Working alone, one person takes 6 hours longer than the other. Working alone, how long (in hours)would it take each person to complete the task? Round your answer to two decimal places.

Accepted Answer

A)  6.91 hours and 6.91 hours 
B)  5.47 hours and 11.47 hours 
C)  6.91 hours and 12.91 hours 
D)  6.47 hours and 11.47 hours 
E)  3.45 hours and 9.45 hours 
A)  6.91 hours and 6.91 hours 
B)  5.47 hours and 11.47 hours 
C)  6.91 hours and 12.91 hours 
D)  6.47 hours and 11.47 hours 
E)  3.45 hours and 9.45 hours

Question 17

Solve $x ^ { 2 } - 6 x + 9 = 0$ by factoring.

Accepted Answer

A)  $x = 3 , x = - 3$ 
B)  x=3 
C)  x=-3 
D)  $x = 0 , x = 3$ 
E)  $x = 3 , x = \frac { 3 } { 2 }$ 
A)  $x = 3 , x = - 3$ 
B)  x=3 
C)  x=-3 
D)  $x = 0 , x = 3$ 
E)  $x = 3 , x = \frac { 3 } { 2 }$

Question 18

Solve the equation $( x - 5 ) ^ { 2 } = - 8$ by using the Square Root Property.

Accepted Answer

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

Question 19

Solve the equation by using the Square Root Property. $9 u ^ { 2 } + 30 = 0$

Accepted Answer

A)  $u = \pm \sqrt { 30 }$ 
B)  $u = \pm \frac { \sqrt { 30 } } { 9 } i$ 
C)  $u = \pm \frac { \sqrt { 30 } } { 3 }$ 
D)  $u = \pm \frac { \sqrt { 30 } } { 9 }$ 
E)  $u = \pm \frac { \sqrt { 30 } } { 3 } i$ 
A)  $u = \pm \sqrt { 30 }$ 
B)  $u = \pm \frac { \sqrt { 30 } } { 9 } i$ 
C)  $u = \pm \frac { \sqrt { 30 } } { 3 }$ 
D)  $u = \pm \frac { \sqrt { 30 } } { 9 }$ 
E)  $u = \pm \frac { \sqrt { 30 } } { 3 } i$

Question 20

Identify the transformations of the graph of $f ( x ) = x ^ { 2 }$ that would produce the graph of $h ( x ) = - ( x + 3 ) ^ { 2 } + 4$ .

Accepted Answer

A) horizontal shift 3 units left; vertical shift 4 units upward 
B) horizontal shift 3 units right; reflection in the x -axis; vertical shift 4 units downward 
C) horizontal shift 4 units right; vertical shift 3 units downward 
D) horizontal shift 4 units left; reflection in the x -axis; vertical shift 3 units upward 
E) horizontal shift 3 units left; reflection in the x -axis; vertical shift 4 units upward 
A) horizontal shift 3 units left; vertical shift 4 units upward 
B) horizontal shift 3 units right; reflection in the x -axis; vertical shift 4 units downward 
C) horizontal shift 4 units right; vertical shift 3 units downward 
D) horizontal shift 4 units left; reflection in the x -axis; vertical shift 3 units upward 
E) horizontal shift 3 units left; reflection in the x -axis; vertical shift 4 units upward

Use a graphing calculator to determine the number of real solutions of the quadratic equation $7 x ^ { 2 } - 6 x - 6 = 0$ .

Use a graphing calculator to approximate the values of x that satisfy the inequality $- 5 x ^ { 2 } + 45 x - 9 > - 14$ . Round all numerical values in your answer to three decimal places, where applicable.

Use the discriminant to determine the number of real solutions of $x ^ { 2 } - 2 x + 7 = 0$ .

Solve the inequality $x ^ { 2 } + 2 x + 1 \geq 0$ and graph the solution on the real number line. (The inequality may have no solution.)

Graph the solution to the inequality $x ^ { 2 } - 3 x + 3 \leq 7$ .

Use the Quadratic Formula to solve $12 x ^ { 2 } - 12 x + 3 = 0$ .

Graph the solution to the inequality on the real number line. $x ^ { 2 } + 3 x \geq 0$

Solve the equation $x ^ { 2 } - 4 x - 3 = 0$ 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.)

Use a graphing calculator to solve the rational inequality $x + \frac { 3 } { x } > 4$ . Round all numerical values in your answer to three decimal places, where applicable.

Solve the equation of quadratic form. $x - 4 \sqrt { x } - 12 = 0$

Graph $y = - \left( x ^ { 2 } - 2 x - 6 \right)$ .

Use the discriminant to determine the number of real solutions of $18 x ^ { 2 } - 12 x + 2 = 0$ .

Find all real and complex solutions of the quadratic equation $( p - 3 ) ^ { 2 } - 243 = 0$ .

Solve the equation $x ^ { 4 } - 37 x ^ { 2 } + 36 = 0$ . (Find all real and complex solutions.)

Working together, two people can complete a task in 4.5 hours. Working alone, one person takes 6 hours longer than the other. Working alone, how long (in hours)would it take each person to complete the task? Round your answer to two decimal places.

Solve $x ^ { 2 } - 6 x + 9 = 0$ by factoring.

Solve the equation $( x - 5 ) ^ { 2 } = - 8$ by using the Square Root Property.

Solve the equation by using the Square Root Property. $9 u ^ { 2 } + 30 = 0$

Identify the transformations of the graph of $f ( x ) = x ^ { 2 }$ that would produce the graph of $h ( x ) = - ( x + 3 ) ^ { 2 } + 4$ .

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

Use a graphing calculator to determine the number of real solutions of the quadratic equation 7x2−6x−6=07 x ^ { 2 } - 6 x - 6 = 07x2−6x−6=0 .

Use a graphing calculator to approximate the values of x that satisfy the inequality −5x2+45x−9>−14- 5 x ^ { 2 } + 45 x - 9 > - 14−5x2+45x−9>−14 . Round all numerical values in your answer to three decimal places, where applicable.

Use the discriminant to determine the number of real solutions of x2−2x+7=0x ^ { 2 } - 2 x + 7 = 0x2−2x+7=0 .

Solve the inequality x2+2x+1≥0x ^ { 2 } + 2 x + 1 \geq 0x2+2x+1≥0 and graph the solution on the real number line. (The inequality may have no solution.)

Graph the solution to the inequality x2−3x+3≤7x ^ { 2 } - 3 x + 3 \leq 7x2−3x+3≤7 .

Use the Quadratic Formula to solve 12x2−12x+3=012 x ^ { 2 } - 12 x + 3 = 012x2−12x+3=0 .

Graph the solution to the inequality on the real number line. x2+3x≥0x ^ { 2 } + 3 x \geq 0x2+3x≥0

Solve the equation x2−4x−3=0x ^ { 2 } - 4 x - 3 = 0x2−4x−3=0 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.)

Use a graphing calculator to solve the rational inequality x+3x>4x + \frac { 3 } { x } > 4x+x3​>4 . Round all numerical values in your answer to three decimal places, where applicable.

Solve the equation of quadratic form. x−4x−12=0x - 4 \sqrt { x } - 12 = 0x−4x​−12=0

Graph y=−(x2−2x−6)y = - \left( x ^ { 2 } - 2 x - 6 \right)y=−(x2−2x−6) .

Use the discriminant to determine the number of real solutions of 18x2−12x+2=018 x ^ { 2 } - 12 x + 2 = 018x2−12x+2=0 .

Find all real and complex solutions of the quadratic equation (p−3)2−243=0( p - 3 ) ^ { 2 } - 243 = 0(p−3)2−243=0 .

Solve the equation x4−37x2+36=0x ^ { 4 } - 37 x ^ { 2 } + 36 = 0x4−37x2+36=0 . (Find all real and complex solutions.)

Working together, two people can complete a task in 4.5 hours. Working alone, one person takes 6 hours longer than the other. Working alone, how long (in hours)would it take each person to complete the task? Round your answer to two decimal places.

Solve x2−6x+9=0x ^ { 2 } - 6 x + 9 = 0x2−6x+9=0 by factoring.

Solve the equation (x−5)2=−8( x - 5 ) ^ { 2 } = - 8(x−5)2=−8 by using the Square Root Property.

Solve the equation by using the Square Root Property. 9u2+30=09 u ^ { 2 } + 30 = 09u2+30=0

Identify the transformations of the graph of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 that would produce the graph of h(x)=−(x+3)2+4h ( x ) = - ( x + 3 ) ^ { 2 } + 4h(x)=−(x+3)2+4 .

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

Use a graphing calculator to determine the number of real solutions of the quadratic equation $7 x ^ { 2 } - 6 x - 6 = 0$ .

Use a graphing calculator to approximate the values of x that satisfy the inequality $- 5 x ^ { 2 } + 45 x - 9 > - 14$ . Round all numerical values in your answer to three decimal places, where applicable.

Use the discriminant to determine the number of real solutions of $x ^ { 2 } - 2 x + 7 = 0$ .

Solve the inequality $x ^ { 2 } + 2 x + 1 \geq 0$ and graph the solution on the real number line. (The inequality may have no solution.)

Graph the solution to the inequality $x ^ { 2 } - 3 x + 3 \leq 7$ .

Use the Quadratic Formula to solve $12 x ^ { 2 } - 12 x + 3 = 0$ .

Graph the solution to the inequality on the real number line. $x ^ { 2 } + 3 x \geq 0$

Solve the equation $x ^ { 2 } - 4 x - 3 = 0$ 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.)

Use a graphing calculator to solve the rational inequality $x + \frac { 3 } { x } > 4$ . Round all numerical values in your answer to three decimal places, where applicable.

Solve the equation of quadratic form. $x - 4 \sqrt { x } - 12 = 0$

Graph $y = - \left( x ^ { 2 } - 2 x - 6 \right)$ .

Use the discriminant to determine the number of real solutions of $18 x ^ { 2 } - 12 x + 2 = 0$ .

Find all real and complex solutions of the quadratic equation $( p - 3 ) ^ { 2 } - 243 = 0$ .

Solve the equation $x ^ { 4 } - 37 x ^ { 2 } + 36 = 0$ . (Find all real and complex solutions.)

Solve $x ^ { 2 } - 6 x + 9 = 0$ by factoring.

Solve the equation $( x - 5 ) ^ { 2 } = - 8$ by using the Square Root Property.

Solve the equation by using the Square Root Property. $9 u ^ { 2 } + 30 = 0$

Identify the transformations of the graph of $f ( x ) = x ^ { 2 }$ that would produce the graph of $h ( x ) = - ( x + 3 ) ^ { 2 } + 4$ .