Question 1

Solve the inequality. Write the solution set in interval notation.
-$x ^ { 2 } - 6 x \leq - 8$

Accepted Answer

A)  $( - \infty , - 4 ] \cup [ - 2 , \infty )$ 
B)  $[ 2,4 ]$ 
C)  $[ - 4 , - 2 ]$ 
D)  $( - 4 , - 2 )$ 
A)  $( - \infty , - 4 ] \cup [ - 2 , \infty )$ 
B)  $[ 2,4 ]$ 
C)  $[ - 4 , - 2 ]$ 
D)  $( - 4 , - 2 )$

Question 2

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 2 } - 4 x - 21 \leq 0$$

Accepted Answer

A)  $( - \infty , - 3 ] \cup [ 7 , \infty )$ 
B)  $[ 7 , \infty )$ 
C)  $( - \infty , - 3 ]$ 
D)  $[ - 3,7 ]$ 
A)  $( - \infty , - 3 ] \cup [ 7 , \infty )$ 
B)  $[ 7 , \infty )$ 
C)  $( - \infty , - 3 ]$ 
D)  $[ - 3,7 ]$

Question 3

Solve the equation by completing the square.
-$$x ^ { 2 } + x + 2 = 0$$

Accepted Answer

A)  $\left\{ \frac { 1 - \mathrm { i } \sqrt { 7 } } { 2 } , \frac { 1 + \mathrm { i } \sqrt { 7 } } { 2 } \right\}$ 
B)  $\left\{ \frac { 1 - \sqrt { 7 } } { 2 } , \frac { 1 + \sqrt { 7 } } { 2 } \right\}$ 
C)  $\left\{ \frac { - 1 - \sqrt { 7 } } { 2 } , \frac { - 1 + \sqrt { 7 } } { 2 } \right\}$ 
D)  $\left\{ \frac { - 1 - \mathrm { i } \sqrt { 7 } } { 2 } , \frac { - 1 + \mathrm { i } \sqrt { 7 } } { 2 } \right\}$ 
A)  $\left\{ \frac { 1 - \mathrm { i } \sqrt { 7 } } { 2 } , \frac { 1 + \mathrm { i } \sqrt { 7 } } { 2 } \right\}$ 
B)  $\left\{ \frac { 1 - \sqrt { 7 } } { 2 } , \frac { 1 + \sqrt { 7 } } { 2 } \right\}$ 
C)  $\left\{ \frac { - 1 - \sqrt { 7 } } { 2 } , \frac { - 1 + \sqrt { 7 } } { 2 } \right\}$ 
D)  $\left\{ \frac { - 1 - \mathrm { i } \sqrt { 7 } } { 2 } , \frac { - 1 + \mathrm { i } \sqrt { 7 } } { 2 } \right\}$

Question 4

Solve the inequality. Write the solution set in interval notation.
-$$x ( x + 4 ) ( x - 2 ) \leq 0$$

Accepted Answer

A)  $( - 4,0 ) \cup ( 2 , \infty )$ 
B)  $( - \infty , - 4 ] \cup [ 0,2 ]$ 
C)  $( - \infty , - 4 ) \cup ( 0,2 )$ 
D)  $[ - 4,0 ] \cup [ 2 , \infty )$ 
A)  $( - 4,0 ) \cup ( 2 , \infty )$ 
B)  $( - \infty , - 4 ] \cup [ 0,2 ]$ 
C)  $( - \infty , - 4 ) \cup ( 0,2 )$ 
D)  $[ - 4,0 ] \cup [ 2 , \infty )$

Question 5

Use the quadratic formula to solve the equation.
-$$x ( x - 6 ) = 8$$

Accepted Answer

A)  $\{ 3 - \sqrt { 17 } , 3 + \sqrt { 17 } \}$ 
B)  $\{ - 3 + 1 , - 3 - 1 \}$ 
C)  $\{ 3 - 1,3 + 1 \}$ 
D)  $\{ - 3 + \sqrt { 17 } , - 3 - \sqrt { 17 } \}$ 
A)  $\{ 3 - \sqrt { 17 } , 3 + \sqrt { 17 } \}$ 
B)  $\{ - 3 + 1 , - 3 - 1 \}$ 
C)  $\{ 3 - 1,3 + 1 \}$ 
D)  $\{ - 3 + \sqrt { 17 } , - 3 - \sqrt { 17 } \}$

Question 6

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

Accepted Answer

A)  $\left( \frac { 7 } { 2 } , \frac { 139 } { 4 } \right)$ 
B)  $( 7,96 )$ 
C)  $( - 5 , - 2 )$ 
D)  $\left( - \frac { 7 } { 2 } , - \frac { 57 } { 4 } \right)$ 
A)  $\left( \frac { 7 } { 2 } , \frac { 139 } { 4 } \right)$ 
B)  $( 7,96 )$ 
C)  $( - 5 , - 2 )$ 
D)  $\left( - \frac { 7 } { 2 } , - \frac { 57 } { 4 } \right)$

Question 7

Use the discriminant to determine the number and type of solutions of the equation.
-$$5 x ^ { 2 } = - 2 x - 8$$

Accepted Answer

A)  One real solution 
B)  Two complex but not real solutions 
C)  Two real solutions 
A)  One real solution 
B)  Two complex but not real solutions 
C)  Two real solutions

Question 8

Solve the equation by completing the square.
-$$x ^ { 2 } + 18 x = - 58$$

Accepted Answer

A)  $\{ - 18 + \sqrt { 58 } \}$ 
B)  $\{ - 9 - \sqrt { 23 } , - 9 + \sqrt { 23 } \}$ 
C)  $\{ 9 + \sqrt { 23 } \}$ 
D)  $\{ 9 - \sqrt { 58 } , 9 + \sqrt { 58 } \}$ 
A)  $\{ - 18 + \sqrt { 58 } \}$ 
B)  $\{ - 9 - \sqrt { 23 } , - 9 + \sqrt { 23 } \}$ 
C)  $\{ 9 + \sqrt { 23 } \}$ 
D)  $\{ 9 - \sqrt { 58 } , 9 + \sqrt { 58 } \}$

Question 9

Use the quadratic formula to solve the equation.
-$$x ^ { 2 } - 2 x - 15 = 0$$

Accepted Answer

A)  $\{ 3,5 \}$ 
B)  $\{ - 3,5 \}$ 
C)  $\{ 3 , - 5 \}$ 
D)  $\{ - 15,0 \}$ 
A)  $\{ 3,5 \}$ 
B)  $\{ - 3,5 \}$ 
C)  $\{ 3 , - 5 \}$ 
D)  $\{ - 15,0 \}$

Question 10

Match the function with its graph.
-$f ( x ) = - x ^ { 2 } - 2 x$

Accepted Answer

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

Question 11

Solve.
-The hypotenuse of a right triangle is 7 feet long. One leg of the triangle is 3 feet longer then the other leg. Find the perimeter of the triangle.

Accepted Answer

A)  $\frac { 3 } { 2 } + \frac { \sqrt { 89 } } { 2 }$ feet 
B)  $- \frac { 3 } { 2 } + \frac { \sqrt { 89 } } { 2 }$ feet 
C)  $\sqrt { 89 } - 7$ feet 
D)  $\sqrt { 89 } + 7$ feet 
A)  $\frac { 3 } { 2 } + \frac { \sqrt { 89 } } { 2 }$ feet 
B)  $- \frac { 3 } { 2 } + \frac { \sqrt { 89 } } { 2 }$ feet 
C)  $\sqrt { 89 } - 7$ feet 
D)  $\sqrt { 89 } + 7$ feet

Question 12

Solve.
-$$\frac { 8 } { x } + \frac { 1 } { x - 7 } = 1$$

Accepted Answer

A)  $\{ - 8 - 2 \sqrt { 2 } , - 8 + 2 \sqrt { 2 } \}$ 
B)  $\{ 8 - 2 \sqrt { 30 } , 8 + 2 \sqrt { 30 } \}$ 
C)  $\{ - 8 - 2 \sqrt { 30 } , - 8 + 2 \sqrt { 30 } \}$ 
D)  $\{ 8 - 2 \sqrt { 2 } , 8 + 2 \sqrt { 2 } \}$ 
A)  $\{ - 8 - 2 \sqrt { 2 } , - 8 + 2 \sqrt { 2 } \}$ 
B)  $\{ 8 - 2 \sqrt { 30 } , 8 + 2 \sqrt { 30 } \}$ 
C)  $\{ - 8 - 2 \sqrt { 30 } , - 8 + 2 \sqrt { 30 } \}$ 
D)  $\{ 8 - 2 \sqrt { 2 } , 8 + 2 \sqrt { 2 } \}$

Question 13

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
-$f ( x ) = - ( x + 6 ) ^ { 2 }$

Accepted Answer

A)  Vertex: $( - 6,0 )$; axis: $x = - 6$
  
B)  Vertex: $( 0,6 )$; axis: $x = 0$
  
C)  Vertex: $( 6,0 )$; axis: $x = 6$
  
D)  Vertex: $( 0 , - 6 )$; axis: $x = 0$
  
A)  Vertex: $( - 6,0 )$; axis: $x = - 6$
  
B)  Vertex: $( 0,6 )$; axis: $x = 0$
  
C)  Vertex: $( 6,0 )$; axis: $x = 6$
  
D)  Vertex: $( 0 , - 6 )$; axis: $x = 0$

Question 14

Solve.
-Shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut the lawn with a push mower. If they can cut the lawn in 6 hours working together find how long to the nearest tenth of an hour it
Takes for William to cut the lawn alone.

Accepted Answer

A)  10.0 hours 
B)  10.1 hours 
C)  15.0 hours 
D)  15.1 hours 
A)  10.0 hours 
B)  10.1 hours 
C)  15.0 hours 
D)  15.1 hours

Question 15

Solve.
-$$3 x = \sqrt { 7 x + 6 }$$

Accepted Answer

A)  $\left\{ \frac { 7 - \sqrt { 265 } } { 18 } , \frac { 7 + \sqrt { 265 } } { 18 } \right\}$ 
B)  $\left\{ \frac { 7 + i \sqrt { 167 } } { 18 } \right\}$ 
C)  $\left\{ \frac { 7 + \sqrt { 265 } } { 18 } \right\}$ 
D) 
$\left\{ \frac { - 7 - \sqrt { 265 } } { 18 } , \frac { - 7 + \sqrt { 265 } } { 18 } \right\}$ 
A)  $\left\{ \frac { 7 - \sqrt { 265 } } { 18 } , \frac { 7 + \sqrt { 265 } } { 18 } \right\}$ 
B)  $\left\{ \frac { 7 + i \sqrt { 167 } } { 18 } \right\}$ 
C)  $\left\{ \frac { 7 + \sqrt { 265 } } { 18 } \right\}$ 
D) 
$\left\{ \frac { - 7 - \sqrt { 265 } } { 18 } , \frac { - 7 + \sqrt { 265 } } { 18 } \right\}$

Question 16

Solve the equation by completing the square.
-$$x ^ { 2 } + 10 x + 6 = 0$$

Accepted Answer

A)  $\{ 5 - \sqrt { 6 } , 5 + \sqrt { 6 } \}$ 
B)  $\{ - 10 + \sqrt { 6 } \}$ 
C)  $\{ 5 + \sqrt { 19 } \}$ 
D)  $\{ - 5 - \sqrt { 19 } , - 5 + \sqrt { 19 } \}$ 
A)  $\{ 5 - \sqrt { 6 } , 5 + \sqrt { 6 } \}$ 
B)  $\{ - 10 + \sqrt { 6 } \}$ 
C)  $\{ 5 + \sqrt { 19 } \}$ 
D)  $\{ - 5 - \sqrt { 19 } , - 5 + \sqrt { 19 } \}$

Question 17

Solve.
-A ball is thrown upward with an initial velocity of 42 meters per second from a cliff that is 30 meters high. The height of the ball is given by the quadratic equation $\mathrm { h } = - 4.9 \mathrm { t } ^ { 2 } + 42 \mathrm { t } + 30$ where $\mathrm { h }$ is in meters and $\mathrm { t }$ is the time in seconds since the ball was thrown. Find the time it takes the ball to hit the ground. Round your answer to the nearest tenth of a second.

Accepted Answer

A)  $9.2$ seconds 
B)  $9.8$ seconds 
C)  $15.2$ seconds 
D)  $8.6$ seconds 
A)  $9.2$ seconds 
B)  $9.8$ seconds 
C)  $15.2$ seconds 
D)  $8.6$ seconds

Question 18

Match the function with its graph.
-$f ( x ) = - x ^ { 2 } + 2 x + 8$

Accepted Answer

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

Question 19

Solve.
-The diagonal of a rectangular storage room is 7 yards long. If its length is 3 times its width, find the dimensions of the room.

Accepted Answer

A)  $7 \sqrt { 10 }$ yards by $21 \sqrt { 10 }$ yards 
B)  $\frac { \sqrt { 10 } } { 10 }$ yards by $\frac { 3 \sqrt { 10 } } { 10 }$ yards 
C)  $\frac { 3 \sqrt { 10 } } { 10 }$ yards by $\frac { 9 \sqrt { 10 } } { 10 }$ yards 
D)  $\frac { 7 \sqrt { 10 } } { 10 }$ yards by $\frac { 21 \sqrt { 10 } } { 10 }$ yards 
A)  $7 \sqrt { 10 }$ yards by $21 \sqrt { 10 }$ yards 
B)  $\frac { \sqrt { 10 } } { 10 }$ yards by $\frac { 3 \sqrt { 10 } } { 10 }$ yards 
C)  $\frac { 3 \sqrt { 10 } } { 10 }$ yards by $\frac { 9 \sqrt { 10 } } { 10 }$ yards 
D)  $\frac { 7 \sqrt { 10 } } { 10 }$ yards by $\frac { 21 \sqrt { 10 } } { 10 }$ yards

Question 20

Solve.
-The hypotenuse of an isosceles right triangle is 7 feet longer than either of its legs. Find the exact length of each side.

Accepted Answer

A)  7 feet
7 feet
14 feet 
B)  $7 + \sqrt { 2 }$ feet
$7 + \sqrt { 2 }$ feet
$14 + \sqrt { 2 }$ feet 
C)  $7 \sqrt { 2 }$ feet
$7 \sqrt { 2 }$ feet
$7 + 7 \sqrt { 2 }$ feet 
D)  $7 + 7 \sqrt { 2 }$ feet
$7 + 7 \sqrt { 2 }$ feet
$14 + 7 \sqrt { 2 }$ feet 
A)  7 feet
7 feet
14 feet 
B)  $7 + \sqrt { 2 }$ feet
$7 + \sqrt { 2 }$ feet
$14 + \sqrt { 2 }$ feet 
C)  $7 \sqrt { 2 }$ feet
$7 \sqrt { 2 }$ feet
$7 + 7 \sqrt { 2 }$ feet 
D)  $7 + 7 \sqrt { 2 }$ feet
$7 + 7 \sqrt { 2 }$ feet
$14 + 7 \sqrt { 2 }$ feet

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } - 6 x \leq - 8$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } - 4 x - 21 \leq 0$

Solve the equation by completing the square. - $x ^ { 2 } + x + 2 = 0$

Solve the inequality. Write the solution set in interval notation. - $x ( x + 4 ) ( x - 2 ) \leq 0$

Use the quadratic formula to solve the equation. - $x ( x - 6 ) = 8$

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

Use the discriminant to determine the number and type of solutions of the equation. - $5 x ^ { 2 } = - 2 x - 8$

Solve the equation by completing the square. - $x ^ { 2 } + 18 x = - 58$

Use the quadratic formula to solve the equation. - $x ^ { 2 } - 2 x - 15 = 0$

Match the function with its graph. - $f ( x ) = - x ^ { 2 } - 2 x$

Solve. -The hypotenuse of a right triangle is 7 feet long. One leg of the triangle is 3 feet longer then the other leg. Find the perimeter of the triangle.

Solve. - $\frac { 8 } { x } + \frac { 1 } { x - 7 } = 1$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f ( x ) = - ( x + 6 ) ^ { 2 }$ $Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f ( x ) = - ( x + 6 ) ^ { 2 }$

Solve. -Shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut the lawn with a push mower. If they can cut the lawn in 6 hours working together find how long to the nearest tenth of an hour it Takes for William to cut the lawn alone.

Solve. - $3 x = \sqrt { 7 x + 6 }$

Solve the equation by completing the square. - $x ^ { 2 } + 10 x + 6 = 0$

Match the function with its graph. - $f ( x ) = - x ^ { 2 } + 2 x + 8$

Solve. -The diagonal of a rectangular storage room is 7 yards long. If its length is 3 times its width, find the dimensions of the room.

Solve. -The hypotenuse of an isosceles right triangle is 7 feet longer than either of its legs. Find the exact length of each side.

Real Numbers and Algebraic Expressions

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Exam 8: Quadratic Equations and Functions

Solve the inequality. Write the solution set in interval notation. - x2−6x≤−8x ^ { 2 } - 6 x \leq - 8x2−6x≤−8

Solve the inequality. Write the solution set in interval notation. - x2−4x−21≤0x ^ { 2 } - 4 x - 21 \leq 0x2−4x−21≤0

Solve the equation by completing the square. - x2+x+2=0x ^ { 2 } + x + 2 = 0x2+x+2=0

Solve the inequality. Write the solution set in interval notation. - x(x+4)(x−2)≤0x ( x + 4 ) ( x - 2 ) \leq 0x(x+4)(x−2)≤0

Use the quadratic formula to solve the equation. - x(x−6)=8x ( x - 6 ) = 8x(x−6)=8

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

Use the discriminant to determine the number and type of solutions of the equation. - 5x2=−2x−85 x ^ { 2 } = - 2 x - 85x2=−2x−8

Solve the equation by completing the square. - x2+18x=−58x ^ { 2 } + 18 x = - 58x2+18x=−58

Use the quadratic formula to solve the equation. - x2−2x−15=0x ^ { 2 } - 2 x - 15 = 0x2−2x−15=0

Match the function with its graph. - f(x)=−x2−2xf ( x ) = - x ^ { 2 } - 2 xf(x)=−x2−2x