Question 1

Complete the square and factor the resulting perfect-square trinomial. $8 t ^ { 2 } + 120 t$

Accepted Answer

A) ( 8 t + $\frac { 225 } { 4 }$ ) $2$ 
B) ( 8 t - $\frac { 15 } { 2 }$ ) $2$ 
C) ( 8 t + $\frac { 15 } { 2 }$ ) $2$ 
D) ( 8 t - $\frac { 225 } { 4 }$ ) $2$ 
A) ( 8 t + $\frac { 225 } { 4 }$ ) $2$ 
B) ( 8 t - $\frac { 15 } { 2 }$ ) $2$ 
C) ( 8 t + $\frac { 15 } { 2 }$ ) $2$ 
D) ( 8 t - $\frac { 225 } { 4 }$ ) $2$

Question 2

Write the expression in $a + b i$ form. $\frac { \sqrt { 6 } + \sqrt { 5 } i } { \sqrt { 6 } - \sqrt { 5 } i }$

Accepted Answer

A)  $\frac { 30 } { 11 } + \frac { 2 } { 11 } i$ 
B)  $\frac { 1 } { 11 } - 2 \frac { \sqrt { 30 } } { 11 } i$ 
C)  $\frac { 11 } { 30 } + \frac { \sqrt { 30 } } { 11 } i$ 
D)  $\frac { 1 } { 11 } + 2 \frac { \sqrt { 30 } } { 11 } i$ 
E)  $\frac { 11 } { 30 } - \frac { \sqrt { 30 } } { 11 } i$ 
A)  $\frac { 30 } { 11 } + \frac { 2 } { 11 } i$ 
B)  $\frac { 1 } { 11 } - 2 \frac { \sqrt { 30 } } { 11 } i$ 
C)  $\frac { 11 } { 30 } + \frac { \sqrt { 30 } } { 11 } i$ 
D)  $\frac { 1 } { 11 } + 2 \frac { \sqrt { 30 } } { 11 } i$ 
E)  $\frac { 11 } { 30 } - \frac { \sqrt { 30 } } { 11 } i$

Question 3

Use the method of completing the square to solve the quadratic equation. $3 x ^ { 3 } + 7 x - 1 = 0$

Accepted Answer

A)  $x = \frac { - 7 + \sqrt { 61 } } { 2 }$ 
B)  $x = \frac { - 7 \pm \sqrt { 61 } } { 6 }$ 
C)  $x = \frac { \pm 7 \pm \sqrt { 61 } } { 2 }$ 
D)  $x = \frac { \pm 7 + \sqrt { 61 } } { 2 }$ 
E)  $x = \frac { \pm 7 \pm \sqrt { 61 } } { 6 }$ 
A)  $x = \frac { - 7 + \sqrt { 61 } } { 2 }$ 
B)  $x = \frac { - 7 \pm \sqrt { 61 } } { 6 }$ 
C)  $x = \frac { \pm 7 \pm \sqrt { 61 } } { 2 }$ 
D)  $x = \frac { \pm 7 + \sqrt { 61 } } { 2 }$ 
E)  $x = \frac { \pm 7 \pm \sqrt { 61 } } { 6 }$

Question 4

The number of cases of flu seen by doctors at a county health clinic each week during a 10-week period is described by the quadratic function f ( x )= -4 x 2 + 40 x (graphed in the illustration).   What point gives us information of the most cases of flu?

Accepted Answer

A) (5, 100) 
B) (8, 100) 
C) (10, 0) 
D) (5, 0) 
A) (5, 100) 
B) (8, 100) 
C) (10, 0) 
D) (5, 0)

Question 5

Simplify the expression. Enter the answer in a + bi form. $( 5 + i ) ( 2 - 3 i )$

Accepted Answer

A)  $7 + 13 i$ 
B)  $13 - 13 i$ 
C)  $13 + 13 i$ 
D)  $7 - 13 i$ 
A)  $7 + 13 i$ 
B)  $13 - 13 i$ 
C)  $13 + 13 i$ 
D)  $7 - 13 i$

Question 6

Graph the parabola $$y = 4 x ^ { 2 } + 5 x$$ .

Accepted Answer

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

Question 7

Write $\sqrt { - 3 } \sqrt { - 64 }$ in terms of i , perform the indicated operations, and simplify.

Accepted Answer

A)  $- 8 \sqrt { 3 }$ 
B)  $- 8 i \sqrt { 3 }$ 
C)  $24 i$ 
D)  $8 i \sqrt { 3 }$ 
E)  $8 \sqrt { 3 }$ 
A)  $- 8 \sqrt { 3 }$ 
B)  $- 8 i \sqrt { 3 }$ 
C)  $24 i$ 
D)  $8 i \sqrt { 3 }$ 
E)  $8 \sqrt { 3 }$

Question 8

Solve the equation. $5 ( x + 2 ) ^ { 2 } = ( x + 2 ) ^ { 2 } + 32$

Accepted Answer

A)  $2 \pm 2 \times \sqrt { 2 } ( - 0.8,4.8 )$ 
B)  $- 2 + 2 \sqrt { 2 } ( 0.8 )$ 
C)  $2 - 2 \sqrt { 2 } ( 4.8 )$ 
D)  $- 2 \pm 2 \sqrt { 2 } ( - 4.8,0.8 )$ 
E)  $- 2 - 2 \sqrt { 2 } ( - 4.8 )$ 
A)  $2 \pm 2 \times \sqrt { 2 } ( - 0.8,4.8 )$ 
B)  $- 2 + 2 \sqrt { 2 } ( 0.8 )$ 
C)  $2 - 2 \sqrt { 2 } ( 4.8 )$ 
D)  $- 2 \pm 2 \sqrt { 2 } ( - 4.8,0.8 )$ 
E)  $- 2 - 2 \sqrt { 2 } ( - 4.8 )$

Question 9

Use the square root method to solve the equation. $$3 x ^ { 2 } = 48$$

Accepted Answer

A)  $\pm 4$ 
B)  $8$ 
C)  $\pm 8$ 
D)  $- 4$ 
E)  $4$ 
A)  $\pm 4$ 
B)  $8$ 
C)  $\pm 8$ 
D)  $- 4$ 
E)  $4$

Question 10

The area of a circle is numerically equal to 8 times the circumference of the circle. Find the length of a radius of the circle.

Accepted Answer

A) 16 $\pi$ 
B) 17 
C) 16 
D) 15 $\pi$ 
E) 8 $\pi$ 
A) 16 $\pi$ 
B) 17 
C) 16 
D) 15 $\pi$ 
E) 8 $\pi$

Question 11

Simplify the expression. Enter the answer in a + bi form. $( 7 + i ) - ( 1 - 2 i )$

Accepted Answer

A)  $6 + 3 i$ 
B)  $6 - 3 j$ 
C)  $6 + i$ 
D)  $6 - i$ 
A)  $6 + 3 i$ 
B)  $6 - 3 j$ 
C)  $6 + i$ 
D)  $6 - i$

Question 12

Solve the equation. Give the solutions rounded to the nearest hundredth. x  2 + 12 x + 17 = 0

Accepted Answer

A)  $x = - 1.65 , x = - 10.35$ 
B)  $x = - 1.64 , x = - 10.36$ 
C)  $x = 1.64 , x = - 10.37$ 
D)  $x = - 0.64 , x = - 1.65$ 
E)  $x = - 1.64 , \quad x = - 10.35$ 
A)  $x = - 1.65 , x = - 10.35$ 
B)  $x = - 1.64 , x = - 10.36$ 
C)  $x = 1.64 , x = - 10.37$ 
D)  $x = - 0.64 , x = - 1.65$ 
E)  $x = - 1.64 , \quad x = - 10.35$

Question 13

Use the method of completing the square to solve the quadratic equation. $2 x ^ { 2 } + 10 x - 9 = 0$

Accepted Answer

A)  $x = \frac { - 10 \pm \sqrt { 43 } } { 2 }$ 
B)  $x = \frac { \pm 10 \pm \sqrt { 43 } } { 2 }$ 
C)  $x = \frac { \pm 5 \pm \sqrt { 43 } } { 2 }$ 
D)  $x = \frac { 10 \pm \sqrt { 43 } } { 2 }$ 
E)  $x = \frac { - 5 \pm \sqrt { 43 } } { 2 }$ 
A)  $x = \frac { - 10 \pm \sqrt { 43 } } { 2 }$ 
B)  $x = \frac { \pm 10 \pm \sqrt { 43 } } { 2 }$ 
C)  $x = \frac { \pm 5 \pm \sqrt { 43 } } { 2 }$ 
D)  $x = \frac { 10 \pm \sqrt { 43 } } { 2 }$ 
E)  $x = \frac { - 5 \pm \sqrt { 43 } } { 2 }$

Question 14

Solve the following quadratic equation. $t ^ { 2 } + 5 t + 9 = 0$

Accepted Answer

A)  $\{ 2.5 + i \sqrt { 2.75 } , 2.5 - i \sqrt { 2.75 } \}$ 
B)  $\{ 2.5 + i \sqrt { 3 } , 2.5 - i \sqrt { 3 } \}$ 
C)  $\{ - 2.5 + i \sqrt { 2.75 } , - 2.5 - i \sqrt { 2.75 } \}$ 
D)  $\{ - 5 + i \sqrt { 2.75 } , - 5 - i \sqrt { 2.75 } \}$ 
E)  $\{ - 5 + i \sqrt { - 2.75 } , - 5 - i \sqrt { - 2.75 } \}$ 
A)  $\{ 2.5 + i \sqrt { 2.75 } , 2.5 - i \sqrt { 2.75 } \}$ 
B)  $\{ 2.5 + i \sqrt { 3 } , 2.5 - i \sqrt { 3 } \}$ 
C)  $\{ - 2.5 + i \sqrt { 2.75 } , - 2.5 - i \sqrt { 2.75 } \}$ 
D)  $\{ - 5 + i \sqrt { 2.75 } , - 5 - i \sqrt { 2.75 } \}$ 
E)  $\{ - 5 + i \sqrt { - 2.75 } , - 5 - i \sqrt { - 2.75 } \}$

Question 15

Write the number $\sqrt { - 8.6 } - 9.9$ in the form a + bi.

Accepted Answer

A) 9.9 i - 8.6 
B) 9.9 i + 8.6 
C) 9.9 + 8.6 i 
D) 9.9 - 8.6 i 
A) 9.9 i - 8.6 
B) 9.9 i + 8.6 
C) 9.9 + 8.6 i 
D) 9.9 - 8.6 i

Question 16

Look at the graph of the equation $25 x ^ { 2 } - 30 x + 9$ . How many solutions does the equation have? What are they?

Accepted Answer

A) 3 solutions, $\frac { 3 } { 5 }$ , $- \frac { 3 } { 5 }$ , and 0 
B) no solutions 
C) 2 solutions, $\frac { 3 } { 5 }$ and $- \frac { 3 } { 5 }$ 
D) 1 repeated solution, $\frac { 3 } { 5 }$ 
A) 3 solutions, $\frac { 3 } { 5 }$ , $- \frac { 3 } { 5 }$ , and 0 
B) no solutions 
C) 2 solutions, $\frac { 3 } { 5 }$ and $- \frac { 3 } { 5 }$ 
D) 1 repeated solution, $\frac { 3 } { 5 }$

Question 17

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. $5 y ^ { 2 } + 6 y - 3 = 0$

Accepted Answer

A) nonreal complex numbers, complex conjugates 
B) rational, unequal 
C) irrational, unequal 
D) rational, equal 
E) irrational, equal 
A) nonreal complex numbers, complex conjugates 
B) rational, unequal 
C) irrational, unequal 
D) rational, equal 
E) irrational, equal

Question 18

Refer to the graph of f ( x )= 2 x 2  $-$ 2 x $-$ 4 given below and find the y -intercept.   y -intercept = __________

Accepted Answer

Question 19

Write $\sqrt { - 294 }$ in terms of i and simplify.

Accepted Answer

A)  $7 i \sqrt { 6 }$ 
B)  $- 7 i \sqrt { 6 }$ 
C)  $7 \sqrt { 6 }$ 
D)  $42 i$ 
E)  $- 7 \sqrt { 6 i }$ 
A)  $7 i \sqrt { 6 }$ 
B)  $- 7 i \sqrt { 6 }$ 
C)  $7 \sqrt { 6 }$ 
D)  $42 i$ 
E)  $- 7 \sqrt { 6 i }$

Question 20

Simplify the expression. Enter the answer in a + bi form. $( - 5 + \sqrt { - 15 } ) ( 1 - \sqrt { - 15 } )$

Accepted Answer

A)  $10 - 6 \sqrt { 15 i }$ 
B)  $10 + 6 \sqrt { 15 i }$ 
C)  $- 20 + 6 \sqrt { 15 i }$ 
D)  $- 20 - 6 \sqrt { 15 } i$ 
A)  $10 - 6 \sqrt { 15 i }$ 
B)  $10 + 6 \sqrt { 15 i }$ 
C)  $- 20 + 6 \sqrt { 15 i }$ 
D)  $- 20 - 6 \sqrt { 15 } i$

Complete the square and factor the resulting perfect-square trinomial. $8 t ^ { 2 } + 120 t$

Write the expression in $a + b i$ form. $\frac { \sqrt { 6 } + \sqrt { 5 } i } { \sqrt { 6 } - \sqrt { 5 } i }$

Use the method of completing the square to solve the quadratic equation. $3 x ^ { 3 } + 7 x - 1 = 0$

The number of cases of flu seen by doctors at a county health clinic each week during a 10-week period is described by the quadratic function f ( x )= -4 x ²+ 40 x (graphed in the illustration). What point gives us information of the most cases of flu?

Simplify the expression. Enter the answer in a + bi form. $( 5 + i ) ( 2 - 3 i )$

Graph the parabola $y = 4 x ^ { 2 } + 5 x$ .

Write $\sqrt { - 3 } \sqrt { - 64 }$ in terms of i , perform the indicated operations, and simplify.

Solve the equation. $5 ( x + 2 ) ^ { 2 } = ( x + 2 ) ^ { 2 } + 32$

Use the square root method to solve the equation. $3 x ^ { 2 } = 48$

The area of a circle is numerically equal to 8 times the circumference of the circle. Find the length of a radius of the circle.

Simplify the expression. Enter the answer in a + bi form. $( 7 + i ) - ( 1 - 2 i )$

Solve the equation. Give the solutions rounded to the nearest hundredth. x ²+ 12 x + 17 = 0

Use the method of completing the square to solve the quadratic equation. $2 x ^ { 2 } + 10 x - 9 = 0$

Solve the following quadratic equation. $t ^ { 2 } + 5 t + 9 = 0$

Write the number $\sqrt { - 8.6 } - 9.9$ in the form a + bi.

$Look at the graph of the equation 25 x ^ { 2 } - 30 x + 9 . How many solutions does the equation have? What are they?$ Look at the graph of the equation $25 x ^ { 2 } - 30 x + 9$ . How many solutions does the equation have? What are they?

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. $5 y ^ { 2 } + 6 y - 3 = 0$

Refer to the graph of f ( x )= 2 x ² $-$ 2 x $-$ 4 given below and find the y -intercept. y -intercept = __________

Write $\sqrt { - 294 }$ in terms of i and simplify.

Simplify the expression. Enter the answer in a + bi form. $( - 5 + \sqrt { - 15 } ) ( 1 - \sqrt { - 15 } )$

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

Roots and Radicals

Filters

Exam 9: Quadratic Equations

Complete the square and factor the resulting perfect-square trinomial. 8t2+120t8 t ^ { 2 } + 120 t8t2+120t

Write the expression in a+bia + b ia+bi form. 6+5i6−5i\frac { \sqrt { 6 } + \sqrt { 5 } i } { \sqrt { 6 } - \sqrt { 5 } i }6​−5​i6​+5​i​

Use the method of completing the square to solve the quadratic equation. 3x3+7x−1=03 x ^ { 3 } + 7 x - 1 = 03x3+7x−1=0

The number of cases of flu seen by doctors at a county health clinic each week during a 10-week period is described by the quadratic function f ( x )= -4 x 2 + 40 x (graphed in the illustration). What point gives us information of the most cases of flu?

Simplify the expression. Enter the answer in a + bi form. (5+i)(2−3i)( 5 + i ) ( 2 - 3 i )(5+i)(2−3i)

Graph the parabola y=4x2+5xy = 4 x ^ { 2 } + 5 xy=4x2+5x .

Write −3−64\sqrt { - 3 } \sqrt { - 64 }−3​−64​ in terms of i , perform the indicated operations, and simplify.

Solve the equation. 5(x+2)2=(x+2)2+325 ( x + 2 ) ^ { 2 } = ( x + 2 ) ^ { 2 } + 325(x+2)2=(x+2)2+32

Use the square root method to solve the equation. 3x2=483 x ^ { 2 } = 483x2=48

The area of a circle is numerically equal to 8 times the circumference of the circle. Find the length of a radius of the circle.

Simplify the expression. Enter the answer in a + bi form. (7+i)−(1−2i)( 7 + i ) - ( 1 - 2 i )(7+i)−(1−2i)

Solve the equation. Give the solutions rounded to the nearest hundredth. x 2 + 12 x + 17 = 0

Use the method of completing the square to solve the quadratic equation. 2x2+10x−9=02 x ^ { 2 } + 10 x - 9 = 02x2+10x−9=0

Solve the following quadratic equation. t2+5t+9=0t ^ { 2 } + 5 t + 9 = 0t2+5t+9=0

Write the number −8.6−9.9\sqrt { - 8.6 } - 9.9−8.6​−9.9 in the form a + bi.

Look at the graph of the equation 25x2−30x+925 x ^ { 2 } - 30 x + 925x2−30x+9 . How many solutions does the equation have? What are they?

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. 5y2+6y−3=05 y ^ { 2 } + 6 y - 3 = 05y2+6y−3=0

Refer to the graph of f ( x )= 2 x 2 −-− 2 x −-− 4 given below and find the y -intercept. y -intercept = __________

Write −294\sqrt { - 294 }−294​ in terms of i and simplify.

Simplify the expression. Enter the answer in a + bi form. (−5+−15)(1−−15)( - 5 + \sqrt { - 15 } ) ( 1 - \sqrt { - 15 } )(−5+−15​)(1−−15​)

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

Roots and Radicals

Filters

Complete the square and factor the resulting perfect-square trinomial. $8 t ^ { 2 } + 120 t$

Write the expression in $a + b i$ form. $\frac { \sqrt { 6 } + \sqrt { 5 } i } { \sqrt { 6 } - \sqrt { 5 } i }$

Use the method of completing the square to solve the quadratic equation. $3 x ^ { 3 } + 7 x - 1 = 0$

The number of cases of flu seen by doctors at a county health clinic each week during a 10-week period is described by the quadratic function f ( x )= -4 x ²+ 40 x (graphed in the illustration). What point gives us information of the most cases of flu?

Simplify the expression. Enter the answer in a + bi form. $( 5 + i ) ( 2 - 3 i )$

Graph the parabola $y = 4 x ^ { 2 } + 5 x$ .

Write $\sqrt { - 3 } \sqrt { - 64 }$ in terms of i , perform the indicated operations, and simplify.

Solve the equation. $5 ( x + 2 ) ^ { 2 } = ( x + 2 ) ^ { 2 } + 32$

Use the square root method to solve the equation. $3 x ^ { 2 } = 48$

Simplify the expression. Enter the answer in a + bi form. $( 7 + i ) - ( 1 - 2 i )$

Solve the equation. Give the solutions rounded to the nearest hundredth. x ²+ 12 x + 17 = 0

Use the method of completing the square to solve the quadratic equation. $2 x ^ { 2 } + 10 x - 9 = 0$

Solve the following quadratic equation. $t ^ { 2 } + 5 t + 9 = 0$

Write the number $\sqrt { - 8.6 } - 9.9$ in the form a + bi.

$Look at the graph of the equation 25 x ^ { 2 } - 30 x + 9 . How many solutions does the equation have? What are they?$ Look at the graph of the equation $25 x ^ { 2 } - 30 x + 9$ . How many solutions does the equation have? What are they?

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. $5 y ^ { 2 } + 6 y - 3 = 0$

Refer to the graph of f ( x )= 2 x ² $-$ 2 x $-$ 4 given below and find the y -intercept. y -intercept = __________

Write $\sqrt { - 294 }$ in terms of i and simplify.

Simplify the expression. Enter the answer in a + bi form. $( - 5 + \sqrt { - 15 } ) ( 1 - \sqrt { - 15 } )$