Question 1

Use the quadratic formula to solve the equation.
-$$( x + 8 ) ( x - 1 ) = 9$$

Accepted Answer

A)  $\left\{ \frac { - 7 - 3 \sqrt { 13 } } { 2 } , \frac { - 7 + 3 \sqrt { 13 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 7 - 3 i \sqrt { 13 } } { 2 } , \frac { - 7 + 3 i \sqrt { 13 } } { 2 } \right\}$ 
C)  $\left\{ \frac { 7 - 3 i \sqrt { 13 } } { 2 } , \frac { 7 + 3 i \sqrt { 13 } } { 2 } \right\}$ 
D)  $\left\{ \frac { 7 - 3 \sqrt { 13 } } { 2 } , \frac { 7 + 3 \sqrt { 13 } } { 2 } \right\}$ 
A)  $\left\{ \frac { - 7 - 3 \sqrt { 13 } } { 2 } , \frac { - 7 + 3 \sqrt { 13 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 7 - 3 i \sqrt { 13 } } { 2 } , \frac { - 7 + 3 i \sqrt { 13 } } { 2 } \right\}$ 
C)  $\left\{ \frac { 7 - 3 i \sqrt { 13 } } { 2 } , \frac { 7 + 3 i \sqrt { 13 } } { 2 } \right\}$ 
D)  $\left\{ \frac { 7 - 3 \sqrt { 13 } } { 2 } , \frac { 7 + 3 \sqrt { 13 } } { 2 } \right\}$

Question 2

Fill in the blank with one of the words or phrases listed below.

-The graph of $f ( x ) = x ^ { 2 } + k$ has vertexــــــــــــــــــــ

Accepted Answer

A)  $( h , 0 )$ 
B)  $\frac { - b } { 2 a }$ 
C)  $( 0 , \mathrm { k } )$ 
D)  $( h , k )$ 
A)  $( h , 0 )$ 
B)  $\frac { - b } { 2 a }$ 
C)  $( 0 , \mathrm { k } )$ 
D)  $( h , k )$

Question 3

Solve.
-Suppose that an open box is to be made from a square sheet of cardboard by cutting out 3-inch squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 75 cubic inches,
Find the original dimensions of the sheet of cardboard.

Accepted Answer

A)  $5 \sqrt { 3 }$ in. by $5 \sqrt { 3 }$ in. 
B)  $11 \mathrm { in. }$ by $11 \mathrm { in. }$ 
C)  5 in. by 5 in. 
D)  $\sqrt { 5 }$ in. by $\sqrt { 15 }$ in. 
A)  $5 \sqrt { 3 }$ in. by $5 \sqrt { 3 }$ in. 
B)  $11 \mathrm { in. }$ by $11 \mathrm { in. }$ 
C)  5 in. by 5 in. 
D)  $\sqrt { 5 }$ in. by $\sqrt { 15 }$ in.

Question 4

Solve the equation.
-$$( x + 6 ) ^ { 2 } = 10$$

Accepted Answer

A)  $\{ 4 \}$ 
B)  $\{ 6 - \sqrt { 10 } , 6 + \sqrt { 10 } \}$ 
C)  $\{ - \sqrt { 10 } , \sqrt { 10 } \}$ 
D)  $\{ - 6 - \sqrt { 10 } , - 6 + \sqrt { 10 } \}$ 
A)  $\{ 4 \}$ 
B)  $\{ 6 - \sqrt { 10 } , 6 + \sqrt { 10 } \}$ 
C)  $\{ - \sqrt { 10 } , \sqrt { 10 } \}$ 
D)  $\{ - 6 - \sqrt { 10 } , - 6 + \sqrt { 10 } \}$

Question 5

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function.
-$f ( x ) = x ^ { 2 } + 4 x - 7$

Accepted Answer

A)  Vertex: $( - 2,3 )$;
$\mathrm { x }$-intercepts: none;
$y$-intercept: $( 0,7 )$
  
B)  Vertex: $( 4,0 )$;
x-intercept: $( 4,0 )$;
$y$-intercept: $( 0,7 )$
  
C)  Vertex: $( - 2 , - 11 )$;
$x$-intercepts: $( - 2 \pm \sqrt { 11 } , 0 )$;
$y$-intercept: $( 0 , - 7 )$
  
D)  Vertex: $\left( - \frac { 1 } { 2 } , - 12 \frac { 1 } { 4 } \right)$;
x-intercepts: $( - 4,0 )$ and (3,0);
$y$-intercept: $( 0 , - 12 )$
  
A)  Vertex: $( - 2,3 )$;
$\mathrm { x }$-intercepts: none;
$y$-intercept: $( 0,7 )$
  
B)  Vertex: $( 4,0 )$;
x-intercept: $( 4,0 )$;
$y$-intercept: $( 0,7 )$
  
C)  Vertex: $( - 2 , - 11 )$;
$x$-intercepts: $( - 2 \pm \sqrt { 11 } , 0 )$;
$y$-intercept: $( 0 , - 7 )$
  
D)  Vertex: $\left( - \frac { 1 } { 2 } , - 12 \frac { 1 } { 4 } \right)$;
x-intercepts: $( - 4,0 )$ and (3,0);
$y$-intercept: $( 0 , - 12 )$

Question 6

Solve.
-$$( 3 x - 2 ) ^ { 2 } - 9 ( 3 x - 2 ) = - 18$$

Accepted Answer

A)  $\left\{ - \frac { 8 } { 3 } , - \frac { 5 } { 3 } \right\}$ 
B)  $\left\{ \frac { 4 } { 3 } , - \frac { 1 } { 3 } \right\}$ 
C)  $\left\{ \frac { 8 } { 3 } , \frac { 5 } { 3 } \right\}$ 
D)  $\left\{ - 2 , \frac { 1 } { 3 } \right\}$ 
A)  $\left\{ - \frac { 8 } { 3 } , - \frac { 5 } { 3 } \right\}$ 
B)  $\left\{ \frac { 4 } { 3 } , - \frac { 1 } { 3 } \right\}$ 
C)  $\left\{ \frac { 8 } { 3 } , \frac { 5 } { 3 } \right\}$ 
D)  $\left\{ - 2 , \frac { 1 } { 3 } \right\}$

Question 7

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
-$f ( x ) = ( x + 3 ) ^ { 2 } - 9$

Accepted Answer

A)  Vertex: $( 3 , - 9 )$; axis: $x = 3$
  
B)  Vertex: $( - 3 , - 9 )$; axis: $x = 3$
  
C)  Vertex: $( 3 , - 9 )$; axis: $x = - 3$
  
D)  Vertex: $( - 3 , - 9 )$; axis: $x = - 3$
  
A)  Vertex: $( 3 , - 9 )$; axis: $x = 3$
  
B)  Vertex: $( - 3 , - 9 )$; axis: $x = 3$
  
C)  Vertex: $( 3 , - 9 )$; axis: $x = - 3$
  
D)  Vertex: $( - 3 , - 9 )$; axis: $x = - 3$

Question 8

Solve.
-$$128 x = \sqrt { 1 - 192 x }$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 128 } \right\}$ 
B)  $\left\{ \frac { 1 } { 64 } \right\}$ 
C)  $\left\{ \frac { 1 } { 256 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 64 } \right\}$ 
A)  $\left\{ \frac { 1 } { 128 } \right\}$ 
B)  $\left\{ \frac { 1 } { 64 } \right\}$ 
C)  $\left\{ \frac { 1 } { 256 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 64 } \right\}$

Question 9

Solve.
-A ball is thrown upward with an initial velocity of 35 meters per second from a cliff that is 70 meters high. The height of the ball is given by the quadratic equation $h = - 4.9 t ^ { 2 } + 35 t + 100$ where $h$ is in meters and $t$ is the time in seconds since the ball was thrown. Find the time that the ball will be 30 meters from the ground. Round your answer to the nearest tenth of a second.

Accepted Answer

A)  $9.4$ seconds 
B)  $9.3$ seconds 
C)  $8.8$ seconds 
D)  $8.9$ seconds 
A)  $9.4$ seconds 
B)  $9.3$ seconds 
C)  $8.8$ seconds 
D)  $8.9$ seconds

Question 10

Solve the inequality. Write the solution set in interval notation.
-$$\frac { x } { x + 4 } \geq 2$$

Accepted Answer

A)  $( - \infty , - 8 ] \cup ( - 4 , \infty )$ 
B)  $[ - 8 , - 4 )$ 
C)  $( - 4,8 ]$ 
D)  $( - \infty , - 4 ) \cup [ 0 , \infty )$ 
A)  $( - \infty , - 8 ] \cup ( - 4 , \infty )$ 
B)  $[ - 8 , - 4 )$ 
C)  $( - 4,8 ]$ 
D)  $( - \infty , - 4 ) \cup [ 0 , \infty )$

Question 11

Solve.
-$$x = \sqrt { 3 x + 40 }$$

Accepted Answer

A)  $\{ 5,8 \}$ 
B)  $\{ - 20 \}$ 
C)  $\{ 8 \}$ 
D)  $\{ - 5,8 \}$ 
A)  $\{ 5,8 \}$ 
B)  $\{ - 20 \}$ 
C)  $\{ 8 \}$ 
D)  $\{ - 5,8 \}$

Question 12

Solve.
-$5 x ^ { 4 } - 317 x ^ { 2 } - 192 = 0$

Accepted Answer

A)  $\left\{ - \frac { \sqrt { 15 } } { 5 } , \frac { \sqrt { 15 } } { 5 } , - 8,8 \right\}$ 
B)  $\left\{ - 8,8 , - \frac { \mathrm { i } \sqrt { 15 } } { 5 } , \frac { \mathrm { i } \sqrt { 15 } } { 5 } \right\}$ 
C)  $\left\{ - 8 \mathrm { i } , 8 \mathrm { i } , - \frac { \mathrm { i } \sqrt { 15 } } { 5 } , \frac { \mathrm { i } \sqrt { 15 } } { 5 } \right\}$ 
D)  $\left\{ 8 , \frac { \mathrm { i } \sqrt { 15 } } { 5 } \right\}$ 
A)  $\left\{ - \frac { \sqrt { 15 } } { 5 } , \frac { \sqrt { 15 } } { 5 } , - 8,8 \right\}$ 
B)  $\left\{ - 8,8 , - \frac { \mathrm { i } \sqrt { 15 } } { 5 } , \frac { \mathrm { i } \sqrt { 15 } } { 5 } \right\}$ 
C)  $\left\{ - 8 \mathrm { i } , 8 \mathrm { i } , - \frac { \mathrm { i } \sqrt { 15 } } { 5 } , \frac { \mathrm { i } \sqrt { 15 } } { 5 } \right\}$ 
D)  $\left\{ 8 , \frac { \mathrm { i } \sqrt { 15 } } { 5 } \right\}$

Question 13

Solve the inequality. Write the solution set in interval notation.
-$$\frac { 3 x - 21 } { x ^ { 2 } - 1 } \geq 0$$

Accepted Answer

A)  $[ - 1,1 ] \cup [ 7 , \infty )$ 
B)  $( - 1,1 ) \cup [ 7 , \infty )$ 
C)  $( \infty , 1 ) \cup [ 7 , \infty )$ 
D)  $( - 1,7 ]$ 
A)  $[ - 1,1 ] \cup [ 7 , \infty )$ 
B)  $( - 1,1 ) \cup [ 7 , \infty )$ 
C)  $( \infty , 1 ) \cup [ 7 , \infty )$ 
D)  $( - 1,7 ]$

Question 14

Fill in the blank with one of the words or phrases listed below.

-The graph of $f ( x ) = ( x - h ) ^ { 2 }$ has vertexـــــــــــــــــــ

Accepted Answer

A)  $( 0 , \mathrm { k } )$ 
B)  $\frac { - b } { 2 a }$ 
C)  $( h , 0 )$ 
D)  $( h , k )$ 
A)  $( 0 , \mathrm { k } )$ 
B)  $\frac { - b } { 2 a }$ 
C)  $( h , 0 )$ 
D)  $( h , k )$

Question 15

Solve the equation.
-$$x ^ { 4 } - 16 x ^ { 2 } - 225 = 0$$

Accepted Answer

A)  $\{ - 5,5 , - 3,3 \}$ 
B)  $\{ - 25,25 , - 9 i , 9 i \}$ 
C)  $\{ - 5,5 , - 3 i , 3 i \}$ 
D)  $\{ - 3,3 , - 5 i , 5 i \}$ 
A)  $\{ - 5,5 , - 3,3 \}$ 
B)  $\{ - 25,25 , - 9 i , 9 i \}$ 
C)  $\{ - 5,5 , - 3 i , 3 i \}$ 
D)  $\{ - 3,3 , - 5 i , 5 i \}$

Question 16

Use the square root property to solve the equation.
$( x + 6 ) ^ { 2 } = - 121$

Accepted Answer

A)  $\{ - 17,5 \}$ 
B)  $\{ - 6 - 11 i , - 6 + 11 i \}$ 
C)  $\{ - 5,17 \}$ 
D)  $\{ 6 - 11 i , 6 + 11 i \}$ 
A)  $\{ - 17,5 \}$ 
B)  $\{ - 6 - 11 i , - 6 + 11 i \}$ 
C)  $\{ - 5,17 \}$ 
D)  $\{ 6 - 11 i , 6 + 11 i \}$

Question 17

Solve.
-$$x ^ { - 2 } - x ^ { - 1 } - 90 = 0$$

Accepted Answer

A)  $\{ - 10,9 \}$ 
B)  $\left\{ - \frac { 1 } { 10 } , \frac { 1 } { 9 } \right\}$ 
C)  $\{ 10 , - 9 \}$ 
D)  $\left\{ \frac { 1 } { 10 } , - \frac { 1 } { 9 } \right\}$ 
A)  $\{ - 10,9 \}$ 
B)  $\left\{ - \frac { 1 } { 10 } , \frac { 1 } { 9 } \right\}$ 
C)  $\{ 10 , - 9 \}$ 
D)  $\left\{ \frac { 1 } { 10 } , - \frac { 1 } { 9 } \right\}$

Question 18

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
-$f ( x ) = ( x + 1 ) ^ { 2 } - 5$

Accepted Answer

A)  Vertex: $( 1 , - 5 )$; axis: $x = 1$
  
B)  Vertex: $( - 5 , - 1 )$; axis: $x = - 5$
  
C)  Vertex: $( - 1 , - 5 )$; axis: $x = - 1$
  
D)  Vertex: $( 5,1 )$; axis: $x = 5$
  
A)  Vertex: $( 1 , - 5 )$; axis: $x = 1$
  
B)  Vertex: $( - 5 , - 1 )$; axis: $x = - 5$
  
C)  Vertex: $( - 1 , - 5 )$; axis: $x = - 1$
  
D)  Vertex: $( 5,1 )$; axis: $x = 5$

Question 19

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 2 } + 7 x + 6 \geq 0$$

Accepted Answer

A)  $( - \infty , - 6 ]$ 
B)  $[ - 6 , - 1 ]$ 
C)  $[ - 1 , \infty )$ 
D)  $( - \infty , - 6 ] \cup [ - 1 , \infty )$ 
A)  $( - \infty , - 6 ]$ 
B)  $[ - 6 , - 1 ]$ 
C)  $[ - 1 , \infty )$ 
D)  $( - \infty , - 6 ] \cup [ - 1 , \infty )$

Question 20

Solve.
-The length of a rectangular storage room is 4 feet longer than its width. If the area of the room is 45 square feet, find its dimensions.

Accepted Answer

A)  6 feet by 10 feet 
B)  4 feet by 8 feet 
C)  5 feet by 9 feet 
D)  4 feet by 10 feet 
A)  6 feet by 10 feet 
B)  4 feet by 8 feet 
C)  5 feet by 9 feet 
D)  4 feet by 10 feet

Use the quadratic formula to solve the equation. - $( x + 8 ) ( x - 1 ) = 9$

Solve. -Suppose that an open box is to be made from a square sheet of cardboard by cutting out 3-inch squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 75 cubic inches, Find the original dimensions of the sheet of cardboard.

Solve the equation. - $( x + 6 ) ^ { 2 } = 10$

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - $f ( x ) = x ^ { 2 } + 4 x - 7$ $Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - f ( x ) = x ^ { 2 } + 4 x - 7$

Solve. - $( 3 x - 2 ) ^ { 2 } - 9 ( 3 x - 2 ) = - 18$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f ( x ) = ( x + 3 ) ^ { 2 } - 9$ $Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f ( x ) = ( x + 3 ) ^ { 2 } - 9$

Solve. - $128 x = \sqrt { 1 - 192 x }$

Solve the inequality. Write the solution set in interval notation. - $\frac { x } { x + 4 } \geq 2$

Solve. - $x = \sqrt { 3 x + 40 }$

Solve. - $5 x ^ { 4 } - 317 x ^ { 2 } - 192 = 0$

Solve the inequality. Write the solution set in interval notation. - $\frac { 3 x - 21 } { x ^ { 2 } - 1 } \geq 0$

Solve the equation. - $x ^ { 4 } - 16 x ^ { 2 } - 225 = 0$

Use the square root property to solve the equation. $( x + 6 ) ^ { 2 } = - 121$

Solve. - $x ^ { - 2 } - x ^ { - 1 } - 90 = 0$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f ( x ) = ( x + 1 ) ^ { 2 } - 5$ $Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f ( x ) = ( x + 1 ) ^ { 2 } - 5$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } + 7 x + 6 \geq 0$

Solve. -The length of a rectangular storage room is 4 feet longer than its width. If the area of the room is 45 square feet, find its dimensions.

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

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Systems of Equations and Inequalities

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Exam 8: Quadratic Equations and Functions

Use the quadratic formula to solve the equation. - (x+8)(x−1)=9( x + 8 ) ( x - 1 ) = 9(x+8)(x−1)=9

Fill in the blank with one of the words or phrases listed below. -The graph of f(x)=x2+kf ( x ) = x ^ { 2 } + kf(x)=x2+k has vertexــــــــــــــــــــ

Solve. -Suppose that an open box is to be made from a square sheet of cardboard by cutting out 3-inch squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 75 cubic inches, Find the original dimensions of the sheet of cardboard.

Solve the equation. - (x+6)2=10( x + 6 ) ^ { 2 } = 10(x+6)2=10

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - f(x)=x2+4x−7f ( x ) = x ^ { 2 } + 4 x - 7f(x)=x2+4x−7

Solve. - (3x−2)2−9(3x−2)=−18( 3 x - 2 ) ^ { 2 } - 9 ( 3 x - 2 ) = - 18(3x−2)2−9(3x−2)=−18

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=(x+3)2−9f ( x ) = ( x + 3 ) ^ { 2 } - 9f(x)=(x+3)2−9

Solve. - 128x=1−192x128 x = \sqrt { 1 - 192 x }128x=1−192x​

Solve the inequality. Write the solution set in interval notation. - xx+4≥2\frac { x } { x + 4 } \geq 2x+4x​≥2

Solve. - x=3x+40x = \sqrt { 3 x + 40 }x=3x+40​

Solve. - 5x4−317x2−192=05 x ^ { 4 } - 317 x ^ { 2 } - 192 = 05x4−317x2−192=0

Solve the inequality. Write the solution set in interval notation. - 3x−21x2−1≥0\frac { 3 x - 21 } { x ^ { 2 } - 1 } \geq 0x2−13x−21​≥0

Fill in the blank with one of the words or phrases listed below. -The graph of f(x)=(x−h)2f ( x ) = ( x - h ) ^ { 2 }f(x)=(x−h)2 has vertexـــــــــــــــــــ

Solve the equation. - x4−16x2−225=0x ^ { 4 } - 16 x ^ { 2 } - 225 = 0x4−16x2−225=0

Use the square root property to solve the equation. (x+6)2=−121( x + 6 ) ^ { 2 } = - 121(x+6)2=−121

Solve. - x−2−x−1−90=0x ^ { - 2 } - x ^ { - 1 } - 90 = 0x−2−x−1−90=0

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=(x+1)2−5f ( x ) = ( x + 1 ) ^ { 2 } - 5f(x)=(x+1)2−5

Solve the inequality. Write the solution set in interval notation. - x2+7x+6≥0x ^ { 2 } + 7 x + 6 \geq 0x2+7x+6≥0