Question 1

Draw the graph of the equation and label the vertex. $y = - 3 x ^ { 2 }$

Accepted Answer

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

Question 2

Solve the equation. $x ^ { 2 } - 5 x + 4 = 0$

Accepted Answer

The answer of Solve the equation. \(x ^ { 2...

Question 3

The area of the wings of a small aircraft is 140 ft2. If the length is 31 ft longer than the width, what are the dimensions of the wings? (This wing is one piece and goes along the top of the aircraft).

Accepted Answer

A)  3 ft × 34 ft 
B)  4 ft × 30 ft 
C)  5 ft × 30 ft 
D)  4 ft × 35 ft 
A)  3 ft × 34 ft 
B)  4 ft × 30 ft 
C)  5 ft × 30 ft 
D)  4 ft × 35 ft

Question 4

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { 64 }$          j

Accepted Answer

The answer of Express the number in terms of j...

Question 5

Solve the equation using the quadratic formula. Check your solution. $6 y ^ { 2 } + y - 3 = 0$

Accepted Answer

A)  $- \frac { 3 } { 3 }$ 
B)  $\frac { 2 } { 3 }$ 
C)  $\frac { 1 } { 3 } , - \frac { 2 } { 3 }$ 
D)  1, $- \frac { 1 } { 3 }$ 
E)  $\frac { 3 } { 2 } , - \frac { 1 } { 3 }$ 
A)  $- \frac { 3 } { 3 }$ 
B)  $\frac { 2 } { 3 }$ 
C)  $\frac { 1 } { 3 } , - \frac { 2 } { 3 }$ 
D)  1, $- \frac { 1 } { 3 }$ 
E)  $\frac { 3 } { 2 } , - \frac { 1 } { 3 }$

Question 6

Draw the graph of the equation and label the vertex. $y = 2 x ^ { 2 } - 10 x + 3$

Accepted Answer

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

Question 7

A border of uniform width is built around a rectangular garden that measures 19 ft by 36 ft. (see Illustration). The area of the border is 804 ft 2. Find the width of the border, y.

Accepted Answer

A)  7 ft 
B)  4 ft 
C)  6 ft 
D)  5 ft 
E)  37 ft 
A)  7 ft 
B)  4 ft 
C)  6 ft 
D)  5 ft 
E)  37 ft

Question 8

Draw the graph of the equation and label the vertex. $y = - 2 x ^ { 2 } - 10 x + 10$

Accepted Answer

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

Question 9

Solve the equation using the quadratic formula. Check your solution. $6 z ^ { 2 } + z - 1 = 0$

Accepted Answer

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

Question 10

Draw the graph of the equation and label the vertex. $y = 3 x ^ { 2 } - 6 x - 13$

Accepted Answer

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

Question 11

The dimensions of a door are $4 \mathrm { ft }$ by $7 \mathrm { ft } 6 \text { in }$ . If the same amount is added to each dimension of the door, the area is increased by $19.5 \mathrm { ft } ^ { 2 }$ Find the dimensions of the new door.

Accepted Answer

A)  $5.5 \mathrm { ft } \times 9 \mathrm { ft }$ 
B)  $4.5 \mathrm { ft } \times 8 \mathrm { ft }$ 
C)  $6.5 \mathrm { ft } \times 10 \mathrm { ft }$ 
D)  $5.5 \mathrm { ft } \times 8.5 \mathrm { ft }$ 
E)  $4.5 \mathrm { ft } \times 8.5 \mathrm { ft }$ 
A)  $5.5 \mathrm { ft } \times 9 \mathrm { ft }$ 
B)  $4.5 \mathrm { ft } \times 8 \mathrm { ft }$ 
C)  $6.5 \mathrm { ft } \times 10 \mathrm { ft }$ 
D)  $5.5 \mathrm { ft } \times 8.5 \mathrm { ft }$ 
E)  $4.5 \mathrm { ft } \times 8.5 \mathrm { ft }$

Question 12

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $- 3 x ^ { 2 } + 2 x + 7 = 0$

Accepted Answer

A)  -1.23, 1.90 
B)  -1.10, 1.83 
C)  -1.10, 1.90 
D)  -1.23 , 1.83 
E)  -1.23 
A)  -1.23, 1.90 
B)  -1.10, 1.83 
C)  -1.10, 1.90 
D)  -1.23 , 1.83 
E)  -1.23

Question 13

Find the value of a, b, and c in the equation. $18 y ^ { 2 } - y + 28 = 0$

Accepted Answer

A)  a = 18, b = -1, c = 28 
B)  a = 18, b = 1, c = 28 
C)  a = -1, b = 28, c = 18 
D)  a = 18, b = -1, c = -28 
E)  a = 28, b = 18, c = -1 
A)  a = 18, b = -1, c = 28 
B)  a = 18, b = 1, c = 28 
C)  a = -1, b = 28, c = 18 
D)  a = 18, b = -1, c = -28 
E)  a = 28, b = 18, c = -1

Question 14

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $x ^ { 2 } + 12 x + 85 = 0$ x = _____ $\pm$ ______j

Accepted Answer

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

Question 15

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $2 x ^ { 2 } + x + 4 = 0$ x = ____ $\pm$ ____j

Accepted Answer

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

Question 16

Determine the nature of the roots of the quadratic equation without solving it. $3 x ^ { 2 } + 8 = x$

Accepted Answer

A)  two rational roots 
B)  one rational root 
C)  two irrational roots 
D)  two imaginary roots 
A)  two rational roots 
B)  one rational root 
C)  two irrational roots 
D)  two imaginary roots

Question 17

Solve the equation using the quadratic formula. Check your solution. $3 x ^ { 2 } - 75 = 0$

Accepted Answer

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

Question 18

Simplify. $j ^ { 23 }$

Accepted Answer

The answer of Simplify. $j ^ { 23 }$...

Question 19

Simplify. $j ^ { 17 }$

Accepted Answer

A)  -1 
B)  - j 
C)  j 
D)  j3 
E)  1 
A)  -1 
B)  - j 
C)  j 
D)  j3 
E)  1

Question 20

A square is cut out of each corner of a rectangular sheet of aluminum that is 30 cm by 90 cm.(See Illustration) The sides are folded up to form a rectangular container with no top. The area of the bottom of the container is 1,600 cm 2. What are the dimensions of each cut-out square? Find the volume of the container. (V = lwh)

Accepted Answer

A)  The side of cut-out square is 7.00 cm. The volume of the container is 8,030.00 cm 3. 
B)  The side of cut-out square is 5.00 cm. The volume of the container is 16,000.00 cm 3. 
C)  The side of cut-out square is 5.00 cm. The volume of the container is 8,000.00 cm 3. 
D)  The side of cut-out square is 4.00 cm. The volume of the container is 8,000.00 cm 3. 
E)  The side of cut-out square is 6.00 cm. The volume of the container is 8,020.00 cm 3. 
A)  The side of cut-out square is 7.00 cm. The volume of the container is 8,030.00 cm 3. 
B)  The side of cut-out square is 5.00 cm. The volume of the container is 16,000.00 cm 3. 
C)  The side of cut-out square is 5.00 cm. The volume of the container is 8,000.00 cm 3. 
D)  The side of cut-out square is 4.00 cm. The volume of the container is 8,000.00 cm 3. 
E)  The side of cut-out square is 6.00 cm. The volume of the container is 8,020.00 cm 3.

Draw the graph of the equation and label the vertex. $y = - 3 x ^ { 2 }$

Solve the equation. $x ^ { 2 } - 5 x + 4 = 0$

The area of the wings of a small aircraft is 140 ft². If the length is 31 ft longer than the width, what are the dimensions of the wings? (This wing is one piece and goes along the top of the aircraft).

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { 64 }$ j

Solve the equation using the quadratic formula. Check your solution. $6 y ^ { 2 } + y - 3 = 0$

Draw the graph of the equation and label the vertex. $y = 2 x ^ { 2 } - 10 x + 3$

A border of uniform width is built around a rectangular garden that measures 19 ft by 36 ft. (see Illustration). The area of the border is 804 ft ². Find the width of the border, y.

Draw the graph of the equation and label the vertex. $y = - 2 x ^ { 2 } - 10 x + 10$

Solve the equation using the quadratic formula. Check your solution. $6 z ^ { 2 } + z - 1 = 0$

Draw the graph of the equation and label the vertex. $y = 3 x ^ { 2 } - 6 x - 13$

The dimensions of a door are $4 \mathrm { ft }$ by $7 \mathrm { ft } 6 \text { in }$ . If the same amount is added to each dimension of the door, the area is increased by $19.5 \mathrm { ft } ^ { 2 }$ Find the dimensions of the new door.

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $- 3 x ^ { 2 } + 2 x + 7 = 0$

Find the value of a, b, and c in the equation. $18 y ^ { 2 } - y + 28 = 0$

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $x ^ { 2 } + 12 x + 85 = 0$ x = _ $\pm$ __j

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $2 x ^ { 2 } + x + 4 = 0$ x = $\pm$ j

Determine the nature of the roots of the quadratic equation without solving it. $3 x ^ { 2 } + 8 = x$

Solve the equation using the quadratic formula. Check your solution. $3 x ^ { 2 } - 75 = 0$

Simplify. $j ^ { 23 }$

Simplify. $j ^ { 17 }$

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

Draw the graph of the equation and label the vertex. y=−3x2y = - 3 x ^ { 2 }y=−3x2

Solve the equation. x2−5x+4=0x ^ { 2 } - 5 x + 4 = 0x2−5x+4=0

The area of the wings of a small aircraft is 140 ft2. If the length is 31 ft longer than the width, what are the dimensions of the wings? (This wing is one piece and goes along the top of the aircraft).

Express the number in terms of j (if necessary, round the result to three significant digits). 64\sqrt { 64 }64​ j

Solve the equation using the quadratic formula. Check your solution. 6y2+y−3=06 y ^ { 2 } + y - 3 = 06y2+y−3=0

Draw the graph of the equation and label the vertex. y=2x2−10x+3y = 2 x ^ { 2 } - 10 x + 3y=2x2−10x+3

A border of uniform width is built around a rectangular garden that measures 19 ft by 36 ft. (see Illustration). The area of the border is 804 ft 2. Find the width of the border, y.

Draw the graph of the equation and label the vertex. y=−2x2−10x+10y = - 2 x ^ { 2 } - 10 x + 10y=−2x2−10x+10

Solve the equation using the quadratic formula. Check your solution. 6z2+z−1=06 z ^ { 2 } + z - 1 = 06z2+z−1=0

Draw the graph of the equation and label the vertex. y=3x2−6x−13y = 3 x ^ { 2 } - 6 x - 13y=3x2−6x−13

The dimensions of a door are 4ft4 \mathrm { ft }4ft by 7ft6 in 7 \mathrm { ft } 6 \text { in }7ft6 in . If the same amount is added to each dimension of the door, the area is increased by 19.5ft219.5 \mathrm { ft } ^ { 2 }19.5ft2 Find the dimensions of the new door.

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). −3x2+2x+7=0- 3 x ^ { 2 } + 2 x + 7 = 0−3x2+2x+7=0

Find the value of a, b, and c in the equation. 18y2−y+28=018 y ^ { 2 } - y + 28 = 018y2−y+28=0

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). x2+12x+85=0x ^ { 2 } + 12 x + 85 = 0x2+12x+85=0 x = _____ ±\pm± ______j

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). 2x2+x+4=02 x ^ { 2 } + x + 4 = 02x2+x+4=0 x = ____ ±\pm± ____j

Determine the nature of the roots of the quadratic equation without solving it. 3x2+8=x3 x ^ { 2 } + 8 = x3x2+8=x

Solve the equation using the quadratic formula. Check your solution. 3x2−75=03 x ^ { 2 } - 75 = 03x2−75=0

Simplify. j23j ^ { 23 }j23

Simplify. j17j ^ { 17 }j17

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

Draw the graph of the equation and label the vertex. $y = - 3 x ^ { 2 }$

Solve the equation. $x ^ { 2 } - 5 x + 4 = 0$

The area of the wings of a small aircraft is 140 ft². If the length is 31 ft longer than the width, what are the dimensions of the wings? (This wing is one piece and goes along the top of the aircraft).

Express the number in terms of j (if necessary, round the result to three significant digits). $\sqrt { 64 }$ j

Solve the equation using the quadratic formula. Check your solution. $6 y ^ { 2 } + y - 3 = 0$

Draw the graph of the equation and label the vertex. $y = 2 x ^ { 2 } - 10 x + 3$

A border of uniform width is built around a rectangular garden that measures 19 ft by 36 ft. (see Illustration). The area of the border is 804 ft ². Find the width of the border, y.

Draw the graph of the equation and label the vertex. $y = - 2 x ^ { 2 } - 10 x + 10$

Solve the equation using the quadratic formula. Check your solution. $6 z ^ { 2 } + z - 1 = 0$

Draw the graph of the equation and label the vertex. $y = 3 x ^ { 2 } - 6 x - 13$

The dimensions of a door are $4 \mathrm { ft }$ by $7 \mathrm { ft } 6 \text { in }$ . If the same amount is added to each dimension of the door, the area is increased by $19.5 \mathrm { ft } ^ { 2 }$ Find the dimensions of the new door.

Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $- 3 x ^ { 2 } + 2 x + 7 = 0$

Find the value of a, b, and c in the equation. $18 y ^ { 2 } - y + 28 = 0$

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $x ^ { 2 } + 12 x + 85 = 0$ x = _ $\pm$ __j

Solve the quadratic equation using the quadratic formula (if necessary, round the result to three significant digits). $2 x ^ { 2 } + x + 4 = 0$ x = $\pm$ j

Determine the nature of the roots of the quadratic equation without solving it. $3 x ^ { 2 } + 8 = x$

Solve the equation using the quadratic formula. Check your solution. $3 x ^ { 2 } - 75 = 0$

Simplify. $j ^ { 23 }$

Simplify. $j ^ { 17 }$