Question 1

Write $\sqrt { - \frac { 49 } { 4 } }$ in terms of i and simplify.

Accepted Answer

A)  $\frac { 7 } { 2 }$ 
B)  $- \frac { 7 } { 2 } + i$ 
C)  $\frac { 7 } { 2 } + i$ 
D)  $- \frac { 7 i } { 2 }$ 
E)  $\frac { 7 i } { 2 }$ 
A)  $\frac { 7 } { 2 }$ 
B)  $- \frac { 7 } { 2 } + i$ 
C)  $\frac { 7 } { 2 } + i$ 
D)  $- \frac { 7 i } { 2 }$ 
E)  $\frac { 7 i } { 2 }$ E

Question 2

Find the vertex of the graph of y = 2 x 2  $-$ 24 x + 19.

Accepted Answer

A) (12, 53) 
B) (6, -53) 
C) (-12, -53) 
D) (-6, -53) 
E) (-6, 53) 
A) (12, 53) 
B) (6, -53) 
C) (-12, -53) 
D) (-6, -53) 
E) (-6, 53) B

Question 3

What coefficient indicates whether the graph of the parabola opens upward or downward? $f ( x ) = - 7 x ^ { 2 } + 3 x + 9$

Accepted Answer

-7

Question 4

Graph the equation $y = - 0.5 x ^ { 2 } + 1.5 x + 10$ .

Accepted Answer

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

Question 5

Solve the following quadratic equation using the method that seems most appropriate to you. a $2$ + 3 a = 10

Accepted Answer

A) { -5, 2 } 
B) { -9, 2 } 
C) { -9, 6 } 
D) { -5, 6 } 
E) No real number solutions 
A) { -5, 2 } 
B) { -9, 2 } 
C) { -9, 6 } 
D) { -5, 6 } 
E) No real number solutions

Question 6

The function y = 16 x 2 + 4 x + 10 is written in y = ax 2  $-$ bx $-$ c form. What are a , b and c ?

Accepted Answer

Question 7

What is the 4th step in graphing a quadratic equation $y = a x ^ { 2 } + b x + c$ ?

Accepted Answer

A) Find the intercepts. 
B) Plot points, using symmetry. 
C) Draw the parabola. 
D) Test for opening upward\downward. 
A) Find the intercepts. 
B) Plot points, using symmetry. 
C) Draw the parabola. 
D) Test for opening upward\downward.

Question 8

Use the quadratic formula to find all real solutions of the equation. $2 x ^ { 2 } - 3 x = 4$

Accepted Answer

A)  $\frac { 3 \pm \sqrt { 41 } } { 4 }$ 
B)  $\frac { 3 \pm \sqrt { 41 } } { 2 }$ 
C)  $\frac { - 3 \pm \sqrt { 41 } } { 2 }$ 
D)  $\frac { - 3 \pm \sqrt { 41 } } { 4 }$ 
E) no real solutions 
A)  $\frac { 3 \pm \sqrt { 41 } } { 4 }$ 
B)  $\frac { 3 \pm \sqrt { 41 } } { 2 }$ 
C)  $\frac { - 3 \pm \sqrt { 41 } } { 2 }$ 
D)  $\frac { - 3 \pm \sqrt { 41 } } { 4 }$ 
E) no real solutions

Question 9

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

Accepted Answer

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

Question 10

The height in feet h of a rocket in flight is given by the formula $h = - 16 t ^ { 2 } + 160 t$ , where t is the time of the flight in seconds. How long will it take for the rocket to hit the ground?

Accepted Answer

A) 11 sec 
B) 10 sec 
C) 8 sec 
D) 12 sec 
E) 13 sec 
A) 11 sec 
B) 10 sec 
C) 8 sec 
D) 12 sec 
E) 13 sec

Question 11

Solve the following quadratic equation. $( x - 4 ) ^ { 2 } = - 64$

Accepted Answer

A)  $\{ 8 i , - 8 i \}$ 
B)  $\{ 8 i + 4 , - 8 i + 4 \}$ 
C)  $\{ 4 i + 8 , - 4 i + 8 \}$ 
D)  $\{ 8 i + 4 \}$ 
E)  $\{ 12 , - 12 \}$ 
A)  $\{ 8 i , - 8 i \}$ 
B)  $\{ 8 i + 4 , - 8 i + 4 \}$ 
C)  $\{ 4 i + 8 , - 4 i + 8 \}$ 
D)  $\{ 8 i + 4 \}$ 
E)  $\{ 12 , - 12 \}$

Question 12

Solve the equation by completing the square. $2 x ^ { 2 } = 4 - 8 x$

Accepted Answer

A)  $x = 8$ , $x = - \sqrt { 2 }$ 
B)  $x = - 2 \pm \sqrt { 6 }$ 
C)  $x = 3 \pm \sqrt { 2 }$ 
D)  $x = 2 \pm + \sqrt { 6 }$ 
E)  $x = 2$ , $x = - 2$ 
A)  $x = 8$ , $x = - \sqrt { 2 }$ 
B)  $x = - 2 \pm \sqrt { 6 }$ 
C)  $x = 3 \pm \sqrt { 2 }$ 
D)  $x = 2 \pm + \sqrt { 6 }$ 
E)  $x = 2$ , $x = - 2$

Question 13

Simplify the expression. Enter the answer in a + bi form. $( 6 + \sqrt { - 272 } ) + ( - 2 - \sqrt { - 17 } )$

Accepted Answer

A)  $4 + 3 \sqrt { 17 i }$ 
B)  $4 - 3 \sqrt { 17 i }$ 
C)  $( 4 - 3 \sqrt { 17 } ) i$ 
D)  $( 4 + 3 \sqrt { 17 } ) i$ 
A)  $4 + 3 \sqrt { 17 i }$ 
B)  $4 - 3 \sqrt { 17 i }$ 
C)  $( 4 - 3 \sqrt { 17 } ) i$ 
D)  $( 4 + 3 \sqrt { 17 } ) i$

Question 14

Solve the equation by completing the square. $x ^ { 2 } = 14 - 5 x$

Accepted Answer

A)  $x = 1$ , $x = 10$ 
B)  $x = 2$ , $x = 7$ 
C)  $x = - 7$ , $x = 2$ 
D)  $x = - 10$ , $x = 2$ 
E)  $x = 0$ , $x = 1$ 
A)  $x = 1$ , $x = 10$ 
B)  $x = 2$ , $x = 7$ 
C)  $x = - 7$ , $x = 2$ 
D)  $x = - 10$ , $x = 2$ 
E)  $x = 0$ , $x = 1$

Question 15

Solve the following quadratic equation using the method that seems most appropriate to you. (4 m + 20) $2$ = 256

Accepted Answer

A) { 3, 9 } 
B) { -3, 1 } 
C) { -1, 3 } 
D) { -9, -1 } 
E) No real number solutions 
A) { 3, 9 } 
B) { -3, 1 } 
C) { -1, 3 } 
D) { -9, -1 } 
E) No real number solutions

Question 16

The area of a tennis court is 2,128 square feet (see illustration). The length of the court is $\frac { 19 } { 7 }$ times the width. Find the length and width of the tennis court.

Accepted Answer

A) 94 feet by 25 feet 
B) 82 feet by 26 feet 
C) 85 feet by 25 feet 
D) 76 feet by 22 feet 
E) 76 feet by 28 feet 
A) 94 feet by 25 feet 
B) 82 feet by 26 feet 
C) 85 feet by 25 feet 
D) 76 feet by 22 feet 
E) 76 feet by 28 feet

Question 17

Solve the equation. Enter all roots in bi or a + bi form. $4 x ^ { 2 } + x + 6 = 0$

Accepted Answer

A)  $\frac { - 1 \pm \sqrt { 95 } } { 8 } i$ 
B)  $\frac { - 1 } { 8 } \pm \frac { \sqrt { 95 } } { 8 } i$ 
C)  $\frac { - 1 } { 4 } \pm \frac { \sqrt { 95 } } { 4 } i$ 
D)  $\frac { - 1 \pm \sqrt { 95 } } { 4 } i$ 
A)  $\frac { - 1 \pm \sqrt { 95 } } { 8 } i$ 
B)  $\frac { - 1 } { 8 } \pm \frac { \sqrt { 95 } } { 8 } i$ 
C)  $\frac { - 1 } { 4 } \pm \frac { \sqrt { 95 } } { 4 } i$ 
D)  $\frac { - 1 \pm \sqrt { 95 } } { 4 } i$

Question 18

Write the number 3.9 in the form a + bi.

Accepted Answer

A) 3.9 + 0 i 
B) 3.9 i - 0 
C) 3.9 
D) 3.9 i 
A) 3.9 + 0 i 
B) 3.9 i - 0 
C) 3.9 
D) 3.9 i

Question 19

Use the quadratic formula to find all real solutions of the equation. $x ^ { 2 } - 7 x + 10 = 0$

Accepted Answer

A) x = 10, x = 4 
B) x = 5, x = -2 
C) x = 5, x = 4 
D) x = -5, x = 2 
E) x = 5, x = 2 
A) x = 10, x = 4 
B) x = 5, x = -2 
C) x = 5, x = 4 
D) x = -5, x = 2 
E) x = 5, x = 2

Question 20

Solve the following quadratic equation using the method that seems most appropriate to you. $5 x ^ { 2 } + 2 x - 3 = 0$

Accepted Answer

A)  $\left\{ - 1 , \frac { 3 } { 5 } \right\}$ 
B)  $\left\{ - 1 , \frac { 5 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 5 } { 3 } , 1 \right\}$ 
D)  $\left\{ - \frac { 3 } { 5 } , 1 \right\}$ 
E) No real number solutions 
A)  $\left\{ - 1 , \frac { 3 } { 5 } \right\}$ 
B)  $\left\{ - 1 , \frac { 5 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 5 } { 3 } , 1 \right\}$ 
D)  $\left\{ - \frac { 3 } { 5 } , 1 \right\}$ 
E) No real number solutions

Write $\sqrt { - \frac { 49 } { 4 } }$ in terms of i and simplify.

Find the vertex of the graph of y = 2 x ² $-$ 24 x + 19.

What coefficient indicates whether the graph of the parabola opens upward or downward? $f ( x ) = - 7 x ^ { 2 } + 3 x + 9$

Graph the equation $y = - 0.5 x ^ { 2 } + 1.5 x + 10$ .

Solve the following quadratic equation using the method that seems most appropriate to you. a $2$ + 3 a = 10

The function y = 16 x ²+ 4 x + 10 is written in y = ax² $-$ bx $-$ c form. What are a , b and c ?

What is the 4th step in graphing a quadratic equation $y = a x ^ { 2 } + b x + c$ ?

Use the quadratic formula to find all real solutions of the equation. $2 x ^ { 2 } - 3 x = 4$

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

The height in feet h of a rocket in flight is given by the formula $h = - 16 t ^ { 2 } + 160 t$ , where t is the time of the flight in seconds. How long will it take for the rocket to hit the ground?

Solve the following quadratic equation. $( x - 4 ) ^ { 2 } = - 64$

Solve the equation by completing the square. $2 x ^ { 2 } = 4 - 8 x$

Simplify the expression. Enter the answer in a + bi form. $( 6 + \sqrt { - 272 } ) + ( - 2 - \sqrt { - 17 } )$

Solve the equation by completing the square. $x ^ { 2 } = 14 - 5 x$

Solve the following quadratic equation using the method that seems most appropriate to you. (4 m + 20) $2$ = 256

Solve the equation. Enter all roots in bi or a + bi form. $4 x ^ { 2 } + x + 6 = 0$

Write the number 3.9 in the form a + bi.

Use the quadratic formula to find all real solutions of the equation. $x ^ { 2 } - 7 x + 10 = 0$

Solve the following quadratic equation using the method that seems most appropriate to you. $5 x ^ { 2 } + 2 x - 3 = 0$

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

Write −494\sqrt { - \frac { 49 } { 4 } }−449​​ in terms of i and simplify.

Find the vertex of the graph of y = 2 x 2 −-− 24 x + 19.

What coefficient indicates whether the graph of the parabola opens upward or downward? f(x)=−7x2+3x+9f ( x ) = - 7 x ^ { 2 } + 3 x + 9f(x)=−7x2+3x+9

Graph the equation y=−0.5x2+1.5x+10y = - 0.5 x ^ { 2 } + 1.5 x + 10y=−0.5x2+1.5x+10 .

Solve the following quadratic equation using the method that seems most appropriate to you. a 222 + 3 a = 10

The function y = 16 x 2 + 4 x + 10 is written in y = ax 2 −-− bx −-− c form. What are a , b and c ?

What is the 4th step in graphing a quadratic equation y=ax2+bx+cy = a x ^ { 2 } + b x + cy=ax2+bx+c ?

Use the quadratic formula to find all real solutions of the equation. 2x2−3x=42 x ^ { 2 } - 3 x = 42x2−3x=4

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation. 6z2−5z−6=06 z ^ { 2 } - 5 z - 6 = 06z2−5z−6=0

The height in feet h of a rocket in flight is given by the formula h=−16t2+160th = - 16 t ^ { 2 } + 160 th=−16t2+160t , where t is the time of the flight in seconds. How long will it take for the rocket to hit the ground?

Solve the following quadratic equation. (x−4)2=−64( x - 4 ) ^ { 2 } = - 64(x−4)2=−64

Solve the equation by completing the square. 2x2=4−8x2 x ^ { 2 } = 4 - 8 x2x2=4−8x

Simplify the expression. Enter the answer in a + bi form. (6+−272)+(−2−−17)( 6 + \sqrt { - 272 } ) + ( - 2 - \sqrt { - 17 } )(6+−272​)+(−2−−17​)

Solve the equation by completing the square. x2=14−5xx ^ { 2 } = 14 - 5 xx2=14−5x

Solve the following quadratic equation using the method that seems most appropriate to you. (4 m + 20) 222 = 256

The area of a tennis court is 2,128 square feet (see illustration). The length of the court is 197\frac { 19 } { 7 }719​ times the width. Find the length and width of the tennis court.

Solve the equation. Enter all roots in bi or a + bi form. 4x2+x+6=04 x ^ { 2 } + x + 6 = 04x2+x+6=0

Write the number 3.9 in the form a + bi.

Use the quadratic formula to find all real solutions of the equation. x2−7x+10=0x ^ { 2 } - 7 x + 10 = 0x2−7x+10=0

Solve the following quadratic equation using the method that seems most appropriate to you. 5x2+2x−3=05 x ^ { 2 } + 2 x - 3 = 05x2+2x−3=0

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

Write $\sqrt { - \frac { 49 } { 4 } }$ in terms of i and simplify.

Find the vertex of the graph of y = 2 x ² $-$ 24 x + 19.

What coefficient indicates whether the graph of the parabola opens upward or downward? $f ( x ) = - 7 x ^ { 2 } + 3 x + 9$

Graph the equation $y = - 0.5 x ^ { 2 } + 1.5 x + 10$ .

Solve the following quadratic equation using the method that seems most appropriate to you. a $2$ + 3 a = 10

The function y = 16 x ²+ 4 x + 10 is written in y = ax² $-$ bx $-$ c form. What are a , b and c ?

What is the 4th step in graphing a quadratic equation $y = a x ^ { 2 } + b x + c$ ?

Use the quadratic formula to find all real solutions of the equation. $2 x ^ { 2 } - 3 x = 4$

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

The height in feet h of a rocket in flight is given by the formula $h = - 16 t ^ { 2 } + 160 t$ , where t is the time of the flight in seconds. How long will it take for the rocket to hit the ground?

Solve the following quadratic equation. $( x - 4 ) ^ { 2 } = - 64$

Solve the equation by completing the square. $2 x ^ { 2 } = 4 - 8 x$

Simplify the expression. Enter the answer in a + bi form. $( 6 + \sqrt { - 272 } ) + ( - 2 - \sqrt { - 17 } )$

Solve the equation by completing the square. $x ^ { 2 } = 14 - 5 x$

Solve the following quadratic equation using the method that seems most appropriate to you. (4 m + 20) $2$ = 256

Solve the equation. Enter all roots in bi or a + bi form. $4 x ^ { 2 } + x + 6 = 0$

Use the quadratic formula to find all real solutions of the equation. $x ^ { 2 } - 7 x + 10 = 0$

Solve the following quadratic equation using the method that seems most appropriate to you. $5 x ^ { 2 } + 2 x - 3 = 0$