Question 1

Solve the equation by completing the square.
-$$x ^ { 2 } + 6 x = 31$$

Accepted Answer

A)  $\{ - 3 - 2 \sqrt { 10 } , - 3 + 2 \sqrt { 10 } \}$ 
B)  $\{ - 3 - 2 \sqrt { 20 } , - 3 + 2 \sqrt { 20 } \}$ 
C)  $\{ 2 \sqrt { 10 } - 3,2 \sqrt { 10 } + 3 \}$ 
D)  $\{ - 2 \sqrt { 10 } , 2 \sqrt { 10 } \}$ 
A)  $\{ - 3 - 2 \sqrt { 10 } , - 3 + 2 \sqrt { 10 } \}$ 
B)  $\{ - 3 - 2 \sqrt { 20 } , - 3 + 2 \sqrt { 20 } \}$ 
C)  $\{ 2 \sqrt { 10 } - 3,2 \sqrt { 10 } + 3 \}$ 
D)  $\{ - 2 \sqrt { 10 } , 2 \sqrt { 10 } \}$

Question 2

Solve.
-Shelly can cut a lawn with a riding mower in 2 hours less time than it takes William to cut the lawn with a push mower. If they can cut the lawn in 7 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)  $13.2 \mathrm { hr }$ 
B)  $15.1 \mathrm { hr }$ 
C)  $15.2 \mathrm { hr }$ 
D)  $13.1 \mathrm { hr }$ 
A)  $13.2 \mathrm { hr }$ 
B)  $15.1 \mathrm { hr }$ 
C)  $15.2 \mathrm { hr }$ 
D)  $13.1 \mathrm { hr }$

Question 3

Solve.
-Two pipes can be used to fill a pool. Working together, the two pipes can fill the pool in 7 hours. The larger pipe can fill the pool in 3 hours less time than the smaller pipe can alone. Find the time to the nearest tenth of an
Hour it takes for the smaller pipe working alone to fill the pool.

Accepted Answer

A)  15.7 hours 
B)  15.8 hours 
C)  12.8 hours 
D)  12.7 hours 
A)  15.7 hours 
B)  15.8 hours 
C)  12.8 hours 
D)  12.7 hours

Question 4

Solve the equation by completing the square.
-$$49 x ^ { 2 } + 98 x + 13 = 0$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 7 } , \frac { 13 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 49 } , - \frac { 13 } { 49 } \right\}$ 
C)  $\left\{ - \frac { 13 } { 49 } , \frac { 26 } { 49 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 7 } , - \frac { 13 } { 7 } \right\}$ 
A)  $\left\{ \frac { 1 } { 7 } , \frac { 13 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 49 } , - \frac { 13 } { 49 } \right\}$ 
C)  $\left\{ - \frac { 13 } { 49 } , \frac { 26 } { 49 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 7 } , - \frac { 13 } { 7 } \right\}$

Question 5

Solve.
-An arrow is fired into the air with an initial velocity of 160 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function $h ( t ) = - 16 t ^ { 2 } + 160 t$. Find the maximum height of the arrow.

Accepted Answer

A)  $1200 \mathrm { ft }$ 
B)  $720 \mathrm { ft }$ 
C)  $400 \mathrm { ft }$ 
D)  $80 \mathrm { ft }$ 
A)  $1200 \mathrm { ft }$ 
B)  $720 \mathrm { ft }$ 
C)  $400 \mathrm { ft }$ 
D)  $80 \mathrm { ft }$

Question 6

Find the vertex of the graph of the quadratic function.
-$$f ( x ) = - x ^ { 2 } + x - 8$$

Accepted Answer

A)  $\left( - \frac { 1 } { 2 } , - \frac { 35 } { 4 } \right)$ 
B)  $( - 1 , - 10 )$ 
C)  $( 1 , - 8 )$ 
D)  $\left( \frac { 1 } { 2 } , - \frac { 31 } { 4 } \right)$ 
A)  $\left( - \frac { 1 } { 2 } , - \frac { 35 } { 4 } \right)$ 
B)  $( - 1 , - 10 )$ 
C)  $( 1 , - 8 )$ 
D)  $\left( \frac { 1 } { 2 } , - \frac { 31 } { 4 } \right)$

Question 7

Use the square root property to solve the equation.
$( 11 - 9 x ) ^ { 2 } = 35$

Accepted Answer

A)  $\left\{ \frac { \sqrt { 35 - 11 } } { 9 } , \frac { \sqrt { 35 + 11 } } { 9 } \right\}$ 
B)  $\left\{ \frac { 9 - \sqrt { 35 } } { 11 } , \frac { 9 + \sqrt { 35 } } { 11 } \right\}$ 
C)  $\left\{ \frac { 46 } { 9 } , - \frac { 8 } { 3 } \right\}$ 
D)  $\left\{ \frac { 11 - \sqrt { 35 } } { 9 } , \frac { 11 + \sqrt { 35 } } { 9 } \right\}$ 
A)  $\left\{ \frac { \sqrt { 35 - 11 } } { 9 } , \frac { \sqrt { 35 + 11 } } { 9 } \right\}$ 
B)  $\left\{ \frac { 9 - \sqrt { 35 } } { 11 } , \frac { 9 + \sqrt { 35 } } { 11 } \right\}$ 
C)  $\left\{ \frac { 46 } { 9 } , - \frac { 8 } { 3 } \right\}$ 
D)  $\left\{ \frac { 11 - \sqrt { 35 } } { 9 } , \frac { 11 + \sqrt { 35 } } { 9 } \right\}$

Question 8

Solve the equation by completing the square.
-$$4 \mathrm { x } ^ { 2 } + 1 = 3 \mathrm { x }$$

Accepted Answer

A)  $\left\{ \frac { 3 - i \sqrt { 7 } } { 8 } , \frac { - 3 + i \sqrt { 7 } } { 8 } \right\}$ 
B)  $\left\{ \frac { 3 - i \sqrt { 7 } } { 8 } , \frac { 3 + i \sqrt { 7 } } { 8 } \right\}$ 
C)  $\left\{ \frac { - 3 - \mathrm { i } \sqrt { 7 } } { 8 } , \frac { - 3 + \mathrm { i } \sqrt { 7 } } { 8 } \right\}$ 
D)  $\left\{ \frac { - 3 - \mathrm { i } \sqrt { 7 } } { 8 } , \frac { 3 + \mathrm { i } \sqrt { 7 } } { 8 } \right\}$ 
A)  $\left\{ \frac { 3 - i \sqrt { 7 } } { 8 } , \frac { - 3 + i \sqrt { 7 } } { 8 } \right\}$ 
B)  $\left\{ \frac { 3 - i \sqrt { 7 } } { 8 } , \frac { 3 + i \sqrt { 7 } } { 8 } \right\}$ 
C)  $\left\{ \frac { - 3 - \mathrm { i } \sqrt { 7 } } { 8 } , \frac { - 3 + \mathrm { i } \sqrt { 7 } } { 8 } \right\}$ 
D)  $\left\{ \frac { - 3 - \mathrm { i } \sqrt { 7 } } { 8 } , \frac { 3 + \mathrm { i } \sqrt { 7 } } { 8 } \right\}$

Question 9

Solve.
-Find two numbers whose sum is 120 and whose product is as large as possible. [Hint: Let $x$ and $120 - x$ be the two numbers. Their product can be described by the function $f ( x ) = x ( 120 - x )$.]

Accepted Answer

A)  60 and 180 
B)  $\frac { 1 } { 60 }$ and $\frac { 13 } { 60 }$ 
C)  59 and 61 
D)  60 and 60 
A)  60 and 180 
B)  $\frac { 1 } { 60 }$ and $\frac { 13 } { 60 }$ 
C)  59 and 61 
D)  60 and 60

Question 10

Solve.
-$$x ^ { - 2 } + x ^ { - 1 } = 72$$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 9 } , \frac { 1 } { 8 } \right\}$ 
B)  $\{ 9 , - 8 \}$ 
C)  $\left\{ \frac { 1 } { 9 } , - \frac { 1 } { 8 } \right\}$ 
D)  $\{ - 9,8 \}$ 
A)  $\left\{ - \frac { 1 } { 9 } , \frac { 1 } { 8 } \right\}$ 
B)  $\{ 9 , - 8 \}$ 
C)  $\left\{ \frac { 1 } { 9 } , - \frac { 1 } { 8 } \right\}$ 
D)  $\{ - 9,8 \}$

Question 11

Use the discriminant to determine the number and type of solutions of the equation.
-$$x ^ { 2 } + 2 x + 4 = 0$$

Accepted Answer

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

Question 12

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

Accepted Answer

A)  $( - \infty , - 3 ]$ 
B)  $( - \infty , - 3 ] \cup [ 0 , \infty )$ 
C)  $[ - 3,0 ]$ 
D)  $[ 0 , \infty )$ 
A)  $( - \infty , - 3 ]$ 
B)  $( - \infty , - 3 ] \cup [ 0 , \infty )$ 
C)  $[ - 3,0 ]$ 
D)  $[ 0 , \infty )$

Question 13

Solve.
-The distance, $s ( t )$, in feet traveled by a freely falling object is given by the function $s ( t ) = 16 t ^ { 2 }$, where $t$ is time in seconds. Use this formula to find the time it would take for an object to fall to the ground from a cliff that is 144 feet high.

Accepted Answer

A)  9 seconds 
B)  4 seconds 
C)  2 seconds 
D)  3 seconds 
A)  9 seconds 
B)  4 seconds 
C)  2 seconds 
D)  3 seconds

Question 14

Solve the equation by completing the square.
-$$x ^ { 2 } + 4 x + 20 = 0$$

Accepted Answer

A)  $\{ - 6,2 \}$ 
B)  $\{ - 2 - 4 i , - 2 + 4 i \}$ 
C)  $\{ - 2 + 4 i \}$ 
D)  $\{ - 2 - 16 i , - 2 + 16 i \}$ 
A)  $\{ - 6,2 \}$ 
B)  $\{ - 2 - 4 i , - 2 + 4 i \}$ 
C)  $\{ - 2 + 4 i \}$ 
D)  $\{ - 2 - 16 i , - 2 + 16 i \}$

Question 15

Solve the equation by completing the square.
-$$x ^ { 2 } + 62 = - 18 x$$

Accepted Answer

A)  $\{ - 9 - \sqrt { 19 } , - 9 + \sqrt { 19 } \}$ 
B)  $\{ - 18 + \sqrt { 62 } \}$ 
C)  $\{ 9 + \sqrt { 19 } \}$ 
D)  $\{ 9 - \sqrt { 62 } , 9 + \sqrt { 62 } \}$ 
A)  $\{ - 9 - \sqrt { 19 } , - 9 + \sqrt { 19 } \}$ 
B)  $\{ - 18 + \sqrt { 62 } \}$ 
C)  $\{ 9 + \sqrt { 19 } \}$ 
D)  $\{ 9 - \sqrt { 62 } , 9 + \sqrt { 62 } \}$

Question 16

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
-$f ( x ) = \frac { 1 } { 4 } x ^ { 2 }$

Accepted Answer

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

Question 17

Solve.
-$$x - 9 \sqrt { x } + 18 = 0$$

Accepted Answer

A)  $\{ 3,6 \}$ 
B)  $\{ 9,36 \}$ 
C)  $\{ - 3,3 , - 6,6 \}$ 
D)  $\{ - \sqrt { 3 } , \sqrt { 3 } , - \sqrt { 6 } , \sqrt { 6 } \}$ 
A)  $\{ 3,6 \}$ 
B)  $\{ 9,36 \}$ 
C)  $\{ - 3,3 , - 6,6 \}$ 
D)  $\{ - \sqrt { 3 } , \sqrt { 3 } , - \sqrt { 6 } , \sqrt { 6 } \}$

Question 18

Use the square root property to solve the equation.
$( x - 2 ) ^ { 2 } = 16$

Accepted Answer

A)  $\{ 4 , - 4 \}$ 
B)  $\{ 18 \}$ 
C)  $\{ - 2 , - 6 \}$ 
D)  $\{ 6 , - 2 \}$ 
A)  $\{ 4 , - 4 \}$ 
B)  $\{ 18 \}$ 
C)  $\{ - 2 , - 6 \}$ 
D)  $\{ 6 , - 2 \}$

Question 19

Match the function with its graph.
-$f ( x ) = x ^ { 2 } + 8 x + 7$

Accepted Answer

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

Question 20

Graph the function. Label the vertex.
-$f ( x ) = 2 x ^ { 2 }$

Accepted Answer

A)  Vertex: $( 0,0 )$
  
B)  Vertex: $( 0,2 )$
  
C)  Vertex: $( 0,0 )$
  
D)  Vertex: $( 0,0 )$
  
A)  Vertex: $( 0,0 )$
  
B)  Vertex: $( 0,2 )$
  
C)  Vertex: $( 0,0 )$
  
D)  Vertex: $( 0,0 )$

Solve the equation by completing the square. - $x ^ { 2 } + 6 x = 31$

Solve. -Shelly can cut a lawn with a riding mower in 2 hours less time than it takes William to cut the lawn with a push mower. If they can cut the lawn in 7 hours working together find how long to the nearest tenth of an hour it takes for William to cut the lawn alone.

Solve the equation by completing the square. - $49 x ^ { 2 } + 98 x + 13 = 0$

Solve. -An arrow is fired into the air with an initial velocity of 160 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function $h ( t ) = - 16 t ^ { 2 } + 160 t$ . Find the maximum height of the arrow.

Find the vertex of the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } + x - 8$

Use the square root property to solve the equation. $( 11 - 9 x ) ^ { 2 } = 35$

Solve the equation by completing the square. - $4 \mathrm { x } ^ { 2 } + 1 = 3 \mathrm { x }$

Solve. -Find two numbers whose sum is 120 and whose product is as large as possible. [Hint: Let $x$ and $120 - x$ be the two numbers. Their product can be described by the function $f ( x ) = x ( 120 - x )$ .]

Solve. - $x ^ { - 2 } + x ^ { - 1 } = 72$

Use the discriminant to determine the number and type of solutions of the equation. - $x ^ { 2 } + 2 x + 4 = 0$

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

Solve. -The distance, $s ( t )$ , in feet traveled by a freely falling object is given by the function $s ( t ) = 16 t ^ { 2 }$ , where $t$ is time in seconds. Use this formula to find the time it would take for an object to fall to the ground from a cliff that is 144 feet high.

Solve the equation by completing the square. - $x ^ { 2 } + 4 x + 20 = 0$

Solve the equation by completing the square. - $x ^ { 2 } + 62 = - 18 x$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f ( x ) = \frac { 1 } { 4 } x ^ { 2 }$ $Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f ( x ) = \frac { 1 } { 4 } x ^ { 2 }$

Solve. - $x - 9 \sqrt { x } + 18 = 0$

Use the square root property to solve the equation. $( x - 2 ) ^ { 2 } = 16$

Match the function with its graph. - $f ( x ) = x ^ { 2 } + 8 x + 7$

Graph the function. Label the vertex. - $f ( x ) = 2 x ^ { 2 }$ $Graph the function. Label the vertex. - f ( x ) = 2 x ^ { 2 }$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Exam 8: Quadratic Equations and Functions

Solve the equation by completing the square. - x2+6x=31x ^ { 2 } + 6 x = 31x2+6x=31

Solve. -Shelly can cut a lawn with a riding mower in 2 hours less time than it takes William to cut the lawn with a push mower. If they can cut the lawn in 7 hours working together find how long to the nearest tenth of an hour it takes for William to cut the lawn alone.

Solve the equation by completing the square. - 49x2+98x+13=049 x ^ { 2 } + 98 x + 13 = 049x2+98x+13=0

Solve. -An arrow is fired into the air with an initial velocity of 160 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function h(t)=−16t2+160th ( t ) = - 16 t ^ { 2 } + 160 th(t)=−16t2+160t . Find the maximum height of the arrow.

Find the vertex of the graph of the quadratic function. - f(x)=−x2+x−8f ( x ) = - x ^ { 2 } + x - 8f(x)=−x2+x−8

Use the square root property to solve the equation. (11−9x)2=35( 11 - 9 x ) ^ { 2 } = 35(11−9x)2=35

Solve the equation by completing the square. - 4x2+1=3x4 \mathrm { x } ^ { 2 } + 1 = 3 \mathrm { x }4x2+1=3x

Solve. -Find two numbers whose sum is 120 and whose product is as large as possible. [Hint: Let xxx and 120−x120 - x120−x be the two numbers. Their product can be described by the function f(x)=x(120−x)f ( x ) = x ( 120 - x )f(x)=x(120−x) .]

Solve. - x−2+x−1=72x ^ { - 2 } + x ^ { - 1 } = 72x−2+x−1=72

Use the discriminant to determine the number and type of solutions of the equation. - x2+2x+4=0x ^ { 2 } + 2 x + 4 = 0x2+2x+4=0

Solve the inequality. Write the solution set in interval notation. - x2+3x≥0x ^ { 2 } + 3 x \geq 0x2+3x≥0

Solve the equation by completing the square. - x2+4x+20=0x ^ { 2 } + 4 x + 20 = 0x2+4x+20=0

Solve the equation by completing the square. - x2+62=−18xx ^ { 2 } + 62 = - 18 xx2+62=−18x

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=14x2f ( x ) = \frac { 1 } { 4 } x ^ { 2 }f(x)=41​x2

Solve. - x−9x+18=0x - 9 \sqrt { x } + 18 = 0x−9x​+18=0

Use the square root property to solve the equation. (x−2)2=16( x - 2 ) ^ { 2 } = 16(x−2)2=16

Match the function with its graph. - f(x)=x2+8x+7f ( x ) = x ^ { 2 } + 8 x + 7f(x)=x2+8x+7

Graph the function. Label the vertex. - f(x)=2x2f ( x ) = 2 x ^ { 2 }f(x)=2x2