Question 1

Solve the equation. $x ^ { 2 } - 13 x + 42 = 0$

Accepted Answer

A)  $x = - 6$ , $x = 7$ 
B)  $x = - 6$ , $x = - 7$ 
C)  $x = 6$ , $x = - 7$ 
D)  $x = - 6$ , $x = - 6$ 
E)  $x = 7$ , $x = - 7$ 
A)  $x = - 6$ , $x = 7$ 
B)  $x = - 6$ , $x = - 7$ 
C)  $x = 6$ , $x = - 7$ 
D)  $x = - 6$ , $x = - 6$ 
E)  $x = 7$ , $x = - 7$

Question 2

Draw the graph of the equation and label the vertex. $y = - x ^ { 2 } + 2 x + 12$

Accepted Answer

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

Question 3

Solve the equation using the quadratic formula. Check your solution. $y ^ { 2 } + 5 y - 24 = 0$

Accepted Answer

A)  3, -9 
B)  3, -8 
C)  4, -8 
D)  4, -9 
E)  3 
A)  3, -9 
B)  3, -8 
C)  4, -8 
D)  4, -9 
E)  3

Question 4

Find the value of a, b, and c in the equation. $9 z ^ { 2 } + z - 5 = 0$

Accepted Answer

A)  a = 9, b = -1, c = 5 
B)  a = 9, b = 1, c = -5 
C)  a = -5, b = 9, c = 1 
D)  a = 1, b = 1, c = -5 
E)  a = 1, b = -5, c = 9 
A)  a = 9, b = -1, c = 5 
B)  a = 9, b = 1, c = -5 
C)  a = -5, b = 9, c = 1 
D)  a = 1, b = 1, c = -5 
E)  a = 1, b = -5, c = 9

Question 5

Solve the equation using the quadratic formula. Check your solution. $x ^ { 2 } - x - 42 = 0$

Accepted Answer

A)  x1 = 6, x2 = -7 
B)  x1 = -7, x2 = - 6 
C)  x1 = 5, x2 = -8 
D)  x1 = - 6, x2 = 7 
E)  x1 = 6, x2 = 7 
A)  x1 = 6, x2 = -7 
B)  x1 = -7, x2 = - 6 
C)  x1 = 5, x2 = -8 
D)  x1 = - 6, x2 = 7 
E)  x1 = 6, x2 = 7

Question 6

Solve the equation. $x ^ { 2 } - 13 x = 36$

Accepted Answer

A)  $x = 9$ 
B)  $x = 4$ , $x = 9$ 
C)  $x = 9$ , $x = - 4$ 
D)  $x = - 9$ , $x = - 4$ 
E)  $x = - 9$ , $x = 4$ 
A)  $x = 9$ 
B)  $x = 4$ , $x = 9$ 
C)  $x = 9$ , $x = - 4$ 
D)  $x = - 9$ , $x = - 4$ 
E)  $x = - 9$ , $x = 4$

Question 7

The perimeter of a rectangle is $200$ m, and its area is $2,400 \mathrm {~m} ^ { 2 }$ . Find its dimensions.

Accepted Answer

A)  $45 \mathrm {~m} \times 55 \mathrm {~m}$ 
B)  $35 \mathrm {~m} \times 65 \mathrm {~m}$ 
C)  $40 \mathrm {~m} \times 60 \mathrm {~m}$ 
D)  $40 \mathrm {~m} \times 65 \mathrm {~m}$ 
E)  $35 \mathrm {~m} \times 60 \mathrm {~m}$ 
A)  $45 \mathrm {~m} \times 55 \mathrm {~m}$ 
B)  $35 \mathrm {~m} \times 65 \mathrm {~m}$ 
C)  $40 \mathrm {~m} \times 60 \mathrm {~m}$ 
D)  $40 \mathrm {~m} \times 65 \mathrm {~m}$ 
E)  $35 \mathrm {~m} \times 60 \mathrm {~m}$

Question 8

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $4 x ^ { 2 } + 9 x + 3 = 0$

Accepted Answer

A)  -0.407, -0.59 
B)  0.593, -1.84 
C)  0.593, -2.84 
D)  -0.407, -2.84 
E)  -0.407, -1.84 
A)  -0.407, -0.59 
B)  0.593, -1.84 
C)  0.593, -2.84 
D)  -0.407, -2.84 
E)  -0.407, -1.84

Question 9

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $x ^ { 2 } - x + 3 = 0$

Accepted Answer

A)  $x = 0.5 + 1.58 j , \quad x = 1 - 1.58 j$ 
B)  $x = 0.5 + 1.58 j , \quad x = 0.5 - 1.58 j$ 
C)  $x = 0.5 + 1.66 j , \quad x = 0.5 - 1.66 j$ 
D)  $x = 5 + 1.58 j , \quad x = 5 - 1.58 j$ 
E)  $x = 0.1 + 1.58 j , \quad x = 1 - 1.58 j$ 
A)  $x = 0.5 + 1.58 j , \quad x = 1 - 1.58 j$ 
B)  $x = 0.5 + 1.58 j , \quad x = 0.5 - 1.58 j$ 
C)  $x = 0.5 + 1.66 j , \quad x = 0.5 - 1.66 j$ 
D)  $x = 5 + 1.58 j , \quad x = 5 - 1.58 j$ 
E)  $x = 0.1 + 1.58 j , \quad x = 1 - 1.58 j$

Question 10

A rectangle is 3 ft longer than it is wide. The area of the rectangle is 54 ft 2. Use a quadratic equation to find the dimensions of the rectangle.

Accepted Answer

A)  3 ft, 6 ft 
B)  5.5 ft, 9.5 ft 
C)  6 ft, 9 ft 
D)  8 ft, 11 ft 
E)  5 ft, 10 ft 
A)  3 ft, 6 ft 
B)  5.5 ft, 9.5 ft 
C)  6 ft, 9 ft 
D)  8 ft, 11 ft 
E)  5 ft, 10 ft

Question 11

Solve the equation. $77 x ^ { 2 } + 170 x + 77 = 0$

Accepted Answer

The answer of Solve the equation. \(77 x ^ {...

Question 12

Draw the graph of the equation and label the vertex. $y = x ^ { 2 } - 2$

Accepted Answer

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

Question 13

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). 2x 2 + 1 = x

Accepted Answer

A)  x = 0.250 + 0.661j, x = 0.250 - 0.661j 
B)  x = 0.250 + 0.707j, x = 0.250 - 0.707j 
C)  x = 0.125 + 0.707j, x = 0.125 - 0.707j 
D)  x = 0.125 + 0.661j, x = 0.125 - 0.661j 
A)  x = 0.250 + 0.661j, x = 0.250 - 0.661j 
B)  x = 0.250 + 0.707j, x = 0.250 - 0.707j 
C)  x = 0.125 + 0.707j, x = 0.125 - 0.707j 
D)  x = 0.125 + 0.661j, x = 0.125 - 0.661j

Question 14

A $1,700$ -ft2 storage building $5$ ft high is needed to store yard maintenance equipment. What dimensions should be used to minimize the outside walls?

Accepted Answer

A)  $43.0 \mathrm { ft } \times 43.0 \mathrm { ft }$ 
B)  $41.2 \mathrm { ft } \times 42.5 \mathrm { ft }$ 
C)  $29.2 \mathrm { ft } \times 29.2 \mathrm { ft }$ 
D)  $58.3 \mathrm { ft } \times 58.3 \mathrm { ft }$ 
E)  $41.2 \mathrm { ft } \times 41.2 \mathrm { ft }$ 
A)  $43.0 \mathrm { ft } \times 43.0 \mathrm { ft }$ 
B)  $41.2 \mathrm { ft } \times 42.5 \mathrm { ft }$ 
C)  $29.2 \mathrm { ft } \times 29.2 \mathrm { ft }$ 
D)  $58.3 \mathrm { ft } \times 58.3 \mathrm { ft }$ 
E)  $41.2 \mathrm { ft } \times 41.2 \mathrm { ft }$

Question 15

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $y ^ { 2 } = 19 y + 7$

Accepted Answer

The answer of Solve the equation using the quadratic formula...

Question 16

A rectangular piece of sheet metal is $2$ ft longer than it is wide. (See the figure below.) The area of the piece of sheet metal is $48 \mathrm { ft } ^ { 2 }$ . Find its length and width.   lenght =                 ft
width =                ft

Accepted Answer

The answer of A rectangular piece of sheet metal is...

Question 17

Solve the equation. $x ^ { 2 } - x = 42$

Accepted Answer

A)  $x = 6$ , $x = 7$ 
B)  $x = - 6$ , $x = 7$ 
C)  $x = - 6$ , $x = - 7$ 
D)  $x = - 6$ , $x = - 6$ 
E)  $x = - 6$ 
A)  $x = 6$ , $x = 7$ 
B)  $x = - 6$ , $x = 7$ 
C)  $x = - 6$ , $x = - 7$ 
D)  $x = - 6$ , $x = - 6$ 
E)  $x = - 6$

Question 18

Draw the graph of the equation and label the vertex. $y = - 0.4 x ^ { 2 } + 2.4 x + 0.7$

Accepted Answer

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

Question 19

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 529 }$

Accepted Answer

A)  $529$ j 
B)  $23$ 
C)  - $23$ 
D)  - $23$ j 
E)  $23$ j 
A)  $529$ j 
B)  $23$ 
C)  - $23$ 
D)  - $23$ j 
E)  $23$ j

Question 20

Simplify. $j ^ { 14 }$

Accepted Answer

A)  $- j$ 
B)  $j$ 
C)  $j ^ { 3 }$ 
D)  $- 1$ 
E)  $1$ 
A)  $- j$ 
B)  $j$ 
C)  $j ^ { 3 }$ 
D)  $- 1$ 
E)  $1$

Solve the equation. $x ^ { 2 } - 13 x + 42 = 0$

Draw the graph of the equation and label the vertex. $y = - x ^ { 2 } + 2 x + 12$

Solve the equation using the quadratic formula. Check your solution. $y ^ { 2 } + 5 y - 24 = 0$

Find the value of a, b, and c in the equation. $9 z ^ { 2 } + z - 5 = 0$

Solve the equation using the quadratic formula. Check your solution. $x ^ { 2 } - x - 42 = 0$

Solve the equation. $x ^ { 2 } - 13 x = 36$

The perimeter of a rectangle is $200$ m, and its area is $2,400 \mathrm {~m} ^ { 2 }$ . Find its dimensions.

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $4 x ^ { 2 } + 9 x + 3 = 0$

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $x ^ { 2 } - x + 3 = 0$

A rectangle is 3 ft longer than it is wide. The area of the rectangle is 54 ft ². Use a quadratic equation to find the dimensions of the rectangle.

Solve the equation. $77 x ^ { 2 } + 170 x + 77 = 0$

Draw the graph of the equation and label the vertex. $y = x ^ { 2 } - 2$

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). 2x ² + 1 = x

A $1,700$ -ft² storage building $5$ ft high is needed to store yard maintenance equipment. What dimensions should be used to minimize the outside walls?

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $y ^ { 2 } = 19 y + 7$

Solve the equation. $x ^ { 2 } - x = 42$

Draw the graph of the equation and label the vertex. $y = - 0.4 x ^ { 2 } + 2.4 x + 0.7$

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 529 }$

Simplify. $j ^ { 14 }$

Basic Concepts

Signed Numbers and Powers of 10

The Metric System

Measurement

Polynomials: an Introduction to Algebra

Equations and Formulas

Ratio and Proportion

Graphing Linear Equations

Systems of Linear Equations

Factoring Algebraic Expressions

Geometry

Right Triangle Trigonometry

Trigonometry With Any Angle

Basic Statistics

Binary and Hexadecimal Numbers

Filters

Exam 11: Quadratic Equations

Solve the equation. x2−13x+42=0x ^ { 2 } - 13 x + 42 = 0x2−13x+42=0

Draw the graph of the equation and label the vertex. y=−x2+2x+12y = - x ^ { 2 } + 2 x + 12y=−x2+2x+12

Solve the equation using the quadratic formula. Check your solution. y2+5y−24=0y ^ { 2 } + 5 y - 24 = 0y2+5y−24=0

Find the value of a, b, and c in the equation. 9z2+z−5=09 z ^ { 2 } + z - 5 = 09z2+z−5=0

Solve the equation using the quadratic formula. Check your solution. x2−x−42=0x ^ { 2 } - x - 42 = 0x2−x−42=0

Solve the equation. x2−13x=36x ^ { 2 } - 13 x = 36x2−13x=36

The perimeter of a rectangle is 200200200 m, and its area is 2,400 m22,400 \mathrm {~m} ^ { 2 }2,400 m2 . Find its dimensions.

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). 4x2+9x+3=04 x ^ { 2 } + 9 x + 3 = 04x2+9x+3=0

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). x2−x+3=0x ^ { 2 } - x + 3 = 0x2−x+3=0

A rectangle is 3 ft longer than it is wide. The area of the rectangle is 54 ft 2. Use a quadratic equation to find the dimensions of the rectangle.

Solve the equation. 77x2+170x+77=077 x ^ { 2 } + 170 x + 77 = 077x2+170x+77=0

Draw the graph of the equation and label the vertex. y=x2−2y = x ^ { 2 } - 2y=x2−2

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). 2x 2 + 1 = x

A 1,7001,7001,700 -ft2 storage building 555 ft high is needed to store yard maintenance equipment. What dimensions should be used to minimize the outside walls?

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). y2=19y+7y ^ { 2 } = 19 y + 7y2=19y+7

A rectangular piece of sheet metal is 222 ft longer than it is wide. (See the figure below.) The area of the piece of sheet metal is 48ft248 \mathrm { ft } ^ { 2 }48ft2 . Find its length and width. lenght = ft width = ft

Solve the equation. x2−x=42x ^ { 2 } - x = 42x2−x=42

Draw the graph of the equation and label the vertex. y=−0.4x2+2.4x+0.7y = - 0.4 x ^ { 2 } + 2.4 x + 0.7y=−0.4x2+2.4x+0.7

Express the number in terms of j (if necessary, round the result to three significant digits). −529\sqrt { - 529 }−529​

Simplify. j14j ^ { 14 }j14

Basic Concepts

Signed Numbers and Powers of 10

The Metric System

Measurement

Polynomials: an Introduction to Algebra

Equations and Formulas

Ratio and Proportion

Graphing Linear Equations

Systems of Linear Equations

Factoring Algebraic Expressions

Geometry

Right Triangle Trigonometry

Trigonometry With Any Angle

Basic Statistics

Binary and Hexadecimal Numbers

Filters

Solve the equation. $x ^ { 2 } - 13 x + 42 = 0$

Draw the graph of the equation and label the vertex. $y = - x ^ { 2 } + 2 x + 12$

Solve the equation using the quadratic formula. Check your solution. $y ^ { 2 } + 5 y - 24 = 0$

Find the value of a, b, and c in the equation. $9 z ^ { 2 } + z - 5 = 0$

Solve the equation using the quadratic formula. Check your solution. $x ^ { 2 } - x - 42 = 0$

Solve the equation. $x ^ { 2 } - 13 x = 36$

The perimeter of a rectangle is $200$ m, and its area is $2,400 \mathrm {~m} ^ { 2 }$ . Find its dimensions.

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $4 x ^ { 2 } + 9 x + 3 = 0$

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $x ^ { 2 } - x + 3 = 0$

A rectangle is 3 ft longer than it is wide. The area of the rectangle is 54 ft ². Use a quadratic equation to find the dimensions of the rectangle.

Solve the equation. $77 x ^ { 2 } + 170 x + 77 = 0$

Draw the graph of the equation and label the vertex. $y = x ^ { 2 } - 2$

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). 2x ² + 1 = x

A $1,700$ -ft² storage building $5$ ft high is needed to store yard maintenance equipment. What dimensions should be used to minimize the outside walls?

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $y ^ { 2 } = 19 y + 7$

Solve the equation. $x ^ { 2 } - x = 42$

Draw the graph of the equation and label the vertex. $y = - 0.4 x ^ { 2 } + 2.4 x + 0.7$

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { - 529 }$

Simplify. $j ^ { 14 }$