Question 1

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

Accepted Answer

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

Question 2

Solve.
-The hypotenuse of an isosceles right triangle is 6 feet longer than either of its legs. Find the exact length of each side.

Accepted Answer

A)  $6 \mathrm { ft } , 6 \mathrm { ft } , 12 \mathrm { ft }$ 
B)  $6 \sqrt { 2 } \mathrm { ft } , 6 \sqrt { 2 } \mathrm { ft } , ( 6 + 6 \sqrt { 2 } ) \mathrm { ft }$ 
C)  $( 6 + 6 \sqrt { 2 } ) \mathrm { ft } , ( 6 + 6 \sqrt { 2 } ) \mathrm { ft } , ( 12 + 6 \sqrt { 2 } ) \mathrm { ft }$ 
D)  $( 6 + \sqrt { 2 } ) \mathrm { ft } , ( 6 + \sqrt { 2 } ) \mathrm { ft } , ( 12 + \sqrt { 2 } ) \mathrm { ft }$ 
A)  $6 \mathrm { ft } , 6 \mathrm { ft } , 12 \mathrm { ft }$ 
B)  $6 \sqrt { 2 } \mathrm { ft } , 6 \sqrt { 2 } \mathrm { ft } , ( 6 + 6 \sqrt { 2 } ) \mathrm { ft }$ 
C)  $( 6 + 6 \sqrt { 2 } ) \mathrm { ft } , ( 6 + 6 \sqrt { 2 } ) \mathrm { ft } , ( 12 + 6 \sqrt { 2 } ) \mathrm { ft }$ 
D)  $( 6 + \sqrt { 2 } ) \mathrm { ft } , ( 6 + \sqrt { 2 } ) \mathrm { ft } , ( 12 + \sqrt { 2 } ) \mathrm { ft }$ C

Question 3

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

Accepted Answer

A)  $- 1,1 , - i , i , - 4$ 
B)  $\varnothing$ 
C)  $1 , i , - 4$ 
D)  $- 1,1 , - 4$ 
A)  $- 1,1 , - i , i , - 4$ 
B)  $\varnothing$ 
C)  $1 , i , - 4$ 
D)  $- 1,1 , - 4$ A

Question 4

Match the function with its graph.
-$f ( x ) = x ^ { 2 } - 4 x$

Accepted Answer

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

Question 5

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

Accepted Answer

A)  $\sqrt { 2 }$ 
B)  $- \sqrt { 2 } , \sqrt { 2 }$ 
C)  1 
D)  4 
A)  $\sqrt { 2 }$ 
B)  $- \sqrt { 2 } , \sqrt { 2 }$ 
C)  1 
D)  4

Question 6

Given the accompanying graph of y = f(x), sketch the graph of the following.
-$y = f ( x + 3 ) - 5$
 
$y = f ( x )$

Accepted Answer

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

Question 7

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
-$f(x)=3 x^{2}+5$

Accepted Answer

A)  vertex $( 5,0 )$; axis $x = 5$
  
B)  vertex $( 0,5 )$; axis $x = 5$
  
C)  vertex $( 0,5 )$; axis $x = 0$
  
D)  vertex $( 0,5 )$; axis $x = 0$
  
A)  vertex $( 5,0 )$; axis $x = 5$
  
B)  vertex $( 0,5 )$; axis $x = 5$
  
C)  vertex $( 0,5 )$; axis $x = 0$
  
D)  vertex $( 0,5 )$; axis $x = 0$

Question 8

Graph the function. Find the vertex.
-$G(x)=3(x-3)^{2}-1$

Accepted Answer

A)  vertex: $( 1 , - 3 )$
  
B)  vertex: $( - 3 , - 1 )$
  
C)  vertex: $( 3 , - 1 )$
  
D)  vertex: $( - 1,3 )$
  
A)  vertex: $( 1 , - 3 )$
  
B)  vertex: $( - 3 , - 1 )$
  
C)  vertex: $( 3 , - 1 )$
  
D)  vertex: $( - 1,3 )$

Question 9

Solve.
-Given the diagram shown, approximate to the nearest meter, how many meters of walking distance a person saves by cutting across the lawn instead of walking on the sidewalk.

Accepted Answer

A)  $21 \mathrm {~m}$ 
B)  $33 \mathrm {~m}$ 
C)  $10 \mathrm {~m}$ 
D)  $9 \mathrm {~m}$ 
A)  $21 \mathrm {~m}$ 
B)  $33 \mathrm {~m}$ 
C)  $10 \mathrm {~m}$ 
D)  $9 \mathrm {~m}$

Question 10

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$\frac { 2 } { x - 6 } < 1$

Accepted Answer

A) $(-\infty, 6)$
  
B)  $( 6,8 )$
  
C) $( - \infty , 6 ) \cup ( 8 , \infty )$
  
D)  $( - \infty , 6 ] \cup [ 8 , \infty )$
  
A) $(-\infty, 6)$
  
B)  $( 6,8 )$
  
C) $( - \infty , 6 ) \cup ( 8 , \infty )$
  
D)  $( - \infty , 6 ] \cup [ 8 , \infty )$

Question 11

Solve.
-Find two numbers whose sum is 56 and whose product is as large as possible. [Hint: Let $x$ and $56 - x$ be the two numbers. Their product can be described by the function $f ( x ) = x ( 56 - x )$.]

Accepted Answer

A)  28 and 84 
B)  $\frac { 1 } { 28 }$ and $\frac { 13 } { 28 }$ 
C)  28 and 28 
D)  27 and 29 
A)  28 and 84 
B)  $\frac { 1 } { 28 }$ and $\frac { 13 } { 28 }$ 
C)  28 and 28 
D)  27 and 29

Question 12

Use the square root property to solve the equation.
-$( 3 x + 4 ) ^ { 2 } = 5$

Accepted Answer

A)  $\frac { \sqrt { 5 } - 4 } { 3 } , \frac { \sqrt { 5 } + 4 } { 3 }$ 
B)  $- 3 , \frac { 1 } { 3 }$ 
C)  $\frac { 4 - \sqrt { 5 } } { 3 } , \frac { 4 + \sqrt { 5 } } { 3 }$ 
D)  $\frac { - 4 - \sqrt { 5 } } { 3 } , \frac { - 4 + \sqrt { 5 } } { 3 }$ 
A)  $\frac { \sqrt { 5 } - 4 } { 3 } , \frac { \sqrt { 5 } + 4 } { 3 }$ 
B)  $- 3 , \frac { 1 } { 3 }$ 
C)  $\frac { 4 - \sqrt { 5 } } { 3 } , \frac { 4 + \sqrt { 5 } } { 3 }$ 
D)  $\frac { - 4 - \sqrt { 5 } } { 3 } , \frac { - 4 + \sqrt { 5 } } { 3 }$

Question 13

Solve.
-The cost in millions of dollars for a company to manufacture $x$ thousand automobiles is given by the function $C ( x ) = 4 x ^ { 2 } - 40 x + 200$. Find the number of automobiles that must be produced to minimize the cost.

Accepted Answer

A)  5 thousand automobiles 
B)  10 thousand automobiles 
C)  20 thousand automobiles 
D)  100 thousand automobiles 
A)  5 thousand automobiles 
B)  10 thousand automobiles 
C)  20 thousand automobiles 
D)  100 thousand automobiles

Question 14

Sketch the graph of the quadratic function by finding the vertex, intercepts, and determining if the graph opens upward
or downward.
-$f(x)=-x^{2}+4 x-3$

Accepted Answer

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

Question 15

Solve.
-$x ^ { - 2 } + 4 x ^ { - 1 } + 3 = 0$

Accepted Answer

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

Question 16

Graph the function. Find the vertex, y-intercept, and x-intercepts (if any).
-$F(x)=2 x^{2}-4 x+5$

Accepted Answer

A)  vertex: $( 1,3 )$
x-intercept: $( 0,0 ) , y$-intercept: $( 0,5 )$
  
B)  vertex: $( 1,3 )$
$x$-intercept: none, $y$-intercept: $( 0,5 )$
  
C)  vertex: $( 1,3 )$
$x$-intercept: none, $y$-intercept: $( 0,5 )$
  
D)  vertex: $( 1,3 )$
$x$-intercept: $( 5,0 ) , y$-intercept: none
  
A)  vertex: $( 1,3 )$
x-intercept: $( 0,0 ) , y$-intercept: $( 0,5 )$
  
B)  vertex: $( 1,3 )$
$x$-intercept: none, $y$-intercept: $( 0,5 )$
  
C)  vertex: $( 1,3 )$
$x$-intercept: none, $y$-intercept: $( 0,5 )$
  
D)  vertex: $( 1,3 )$
$x$-intercept: $( 5,0 ) , y$-intercept: none

Question 17

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

Accepted Answer

A)  vertex $( - 1,0 )$; axis $x = - 1$
  
B)  vertex $( 0 , - 1 )$; axis $x = 0$
  
C)  vertex $( 0,1 )$; axis $x = 0$
  
D)  vertex $( 1,0 )$; axis $x = 1$
  
A)  vertex $( - 1,0 )$; axis $x = - 1$
  
B)  vertex $( 0 , - 1 )$; axis $x = 0$
  
C)  vertex $( 0,1 )$; axis $x = 0$
  
D)  vertex $( 1,0 )$; axis $x = 1$

Question 18

Use the square root property to solve the equation.
-$5 x ^ { 2 } + 55 = 0$

Accepted Answer

A)  $- \mathrm { i } \sqrt { 11 } , \mathrm { i } \sqrt { 11 }$ 
B)  $- \sqrt { 11 } , \sqrt { 11 }$ 
C)  $- 11,11$ 
D)  $- 11 \mathrm { i } , 11 \mathrm { i }$ 
A)  $- \mathrm { i } \sqrt { 11 } , \mathrm { i } \sqrt { 11 }$ 
B)  $- \sqrt { 11 } , \sqrt { 11 }$ 
C)  $- 11,11$ 
D)  $- 11 \mathrm { i } , 11 \mathrm { i }$

Question 19

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$\frac { - 3 } { - 3 x - 7 } > 0$

Accepted Answer

A)  $( 0 , \infty )$
  
B)  $\left( - \infty , \frac { 7 } { 3 } \right)$
  
C)  $\left( - \frac { 7 } { 3 } , \infty \right)$
  
D)  $\left( - \infty , - \frac { 3 } { 7 } \right)$
  
A)  $( 0 , \infty )$
  
B)  $\left( - \infty , \frac { 7 } { 3 } \right)$
  
C)  $\left( - \frac { 7 } { 3 } , \infty \right)$
  
D)  $\left( - \infty , - \frac { 3 } { 7 } \right)$

Question 20

Use the square root property to solve the equation.
-$x ^ { 2 } = 112$

Accepted Answer

A)  56 
B)  14 
C)  $- 4 \sqrt { 7 } , 4 \sqrt { 7 }$ 
D)  $4 \sqrt { 7 }$ 
A)  56 
B)  14 
C)  $- 4 \sqrt { 7 } , 4 \sqrt { 7 }$ 
D)  $4 \sqrt { 7 }$

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

Solve. -The hypotenuse of an isosceles right triangle is 6 feet longer than either of its legs. Find the exact length of each side.

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

Match the function with its graph. - $f ( x ) = x ^ { 2 } - 4 x$

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

Given the accompanying graph of y = f(x), sketch the graph of the following. - $y = f ( x + 3 ) - 5$ $y = f ( x )$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f(x)=3 x^{2}+5$ $Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=3 x^{2}+5$

Graph the function. Find the vertex. - $G(x)=3(x-3)^{2}-1$ $Graph the function. Find the vertex. - G(x)=3(x-3)^{2}-1$

Solve. -Given the diagram shown, approximate to the nearest meter, how many meters of walking distance a person saves by cutting across the lawn instead of walking on the sidewalk.

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $\frac { 2 } { x - 6 } < 1$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - \frac { 2 } { x - 6 } < 1$

Solve. -Find two numbers whose sum is 56 and whose product is as large as possible. [Hint: Let $x$ and $56 - x$ be the two numbers. Their product can be described by the function $f ( x ) = x ( 56 - x )$ .]

Use the square root property to solve the equation. - $( 3 x + 4 ) ^ { 2 } = 5$

Solve. -The cost in millions of dollars for a company to manufacture $x$ thousand automobiles is given by the function $C ( x ) = 4 x ^ { 2 } - 40 x + 200$ . Find the number of automobiles that must be produced to minimize the cost.

Solve. - $x ^ { - 2 } + 4 x ^ { - 1 } + 3 = 0$

Graph the function. Find the vertex, y-intercept, and x-intercepts (if any). - $F(x)=2 x^{2}-4 x+5$ $Graph the function. Find the vertex, y-intercept, and x-intercepts (if any). - F(x)=2 x^{2}-4 x+5$

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

Use the square root property to solve the equation. - $5 x ^ { 2 } + 55 = 0$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $\frac { - 3 } { - 3 x - 7 } > 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - \frac { - 3 } { - 3 x - 7 } > 0$

Use the square root property to solve the equation. - $x ^ { 2 } = 112$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 11: Quadratic Equations and Functions

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

Solve. -The hypotenuse of an isosceles right triangle is 6 feet longer than either of its legs. Find the exact length of each side.

Solve the equation. - x5+4x4=x+4x ^ { 5 } + 4 x ^ { 4 } = x + 4x5+4x4=x+4

Match the function with its graph. - f(x)=x2−4xf ( x ) = x ^ { 2 } - 4 xf(x)=x2−4x

Use the square root property to solve the equation. - x2=2x ^ { 2 } = 2x2=2

Given the accompanying graph of y = f(x), sketch the graph of the following. - y=f(x+3)−5y = f ( x + 3 ) - 5y=f(x+3)−5 y=f(x)y = f ( x )y=f(x)

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=3x2+5f(x)=3 x^{2}+5f(x)=3x2+5

Graph the function. Find the vertex. - G(x)=3(x−3)2−1G(x)=3(x-3)^{2}-1G(x)=3(x−3)2−1

Solve. -Given the diagram shown, approximate to the nearest meter, how many meters of walking distance a person saves by cutting across the lawn instead of walking on the sidewalk.

Solve the inequality. Graph the solution set and write the solution set in interval notation. - 2x−6<1\frac { 2 } { x - 6 } < 1x−62​<1

Solve. -Find two numbers whose sum is 56 and whose product is as large as possible. [Hint: Let xxx and 56−x56 - x56−x be the two numbers. Their product can be described by the function f(x)=x(56−x)f ( x ) = x ( 56 - x )f(x)=x(56−x) .]

Use the square root property to solve the equation. - (3x+4)2=5( 3 x + 4 ) ^ { 2 } = 5(3x+4)2=5

Solve. -The cost in millions of dollars for a company to manufacture xxx thousand automobiles is given by the function C(x)=4x2−40x+200C ( x ) = 4 x ^ { 2 } - 40 x + 200C(x)=4x2−40x+200 . Find the number of automobiles that must be produced to minimize the cost.

Sketch the graph of the quadratic function by finding the vertex, intercepts, and determining if the graph opens upward or downward. - f(x)=−x2+4x−3f(x)=-x^{2}+4 x-3f(x)=−x2+4x−3

Solve. - x−2+4x−1+3=0x ^ { - 2 } + 4 x ^ { - 1 } + 3 = 0x−2+4x−1+3=0

Graph the function. Find the vertex, y-intercept, and x-intercepts (if any). - F(x)=2x2−4x+5F(x)=2 x^{2}-4 x+5F(x)=2x2−4x+5

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=x2+1f(x)=x^{2}+1f(x)=x2+1

Use the square root property to solve the equation. - 5x2+55=05 x ^ { 2 } + 55 = 05x2+55=0

Solve the inequality. Graph the solution set and write the solution set in interval notation. - −3−3x−7>0\frac { - 3 } { - 3 x - 7 } > 0−3x−7−3​>0

Use the square root property to solve the equation. - x2=112x ^ { 2 } = 112x2=112

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

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

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

Match the function with its graph. - $f ( x ) = x ^ { 2 } - 4 x$

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

Given the accompanying graph of y = f(x), sketch the graph of the following. - $y = f ( x + 3 ) - 5$ $y = f ( x )$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f(x)=3 x^{2}+5$ $Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=3 x^{2}+5$

Graph the function. Find the vertex. - $G(x)=3(x-3)^{2}-1$ $Graph the function. Find the vertex. - G(x)=3(x-3)^{2}-1$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $\frac { 2 } { x - 6 } < 1$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - \frac { 2 } { x - 6 } < 1$

Solve. -Find two numbers whose sum is 56 and whose product is as large as possible. [Hint: Let $x$ and $56 - x$ be the two numbers. Their product can be described by the function $f ( x ) = x ( 56 - x )$ .]

Use the square root property to solve the equation. - $( 3 x + 4 ) ^ { 2 } = 5$

Solve. -The cost in millions of dollars for a company to manufacture $x$ thousand automobiles is given by the function $C ( x ) = 4 x ^ { 2 } - 40 x + 200$ . Find the number of automobiles that must be produced to minimize the cost.

Solve. - $x ^ { - 2 } + 4 x ^ { - 1 } + 3 = 0$

Graph the function. Find the vertex, y-intercept, and x-intercepts (if any). - $F(x)=2 x^{2}-4 x+5$ $Graph the function. Find the vertex, y-intercept, and x-intercepts (if any). - F(x)=2 x^{2}-4 x+5$

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

Use the square root property to solve the equation. - $5 x ^ { 2 } + 55 = 0$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $\frac { - 3 } { - 3 x - 7 } > 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - \frac { - 3 } { - 3 x - 7 } > 0$

Use the square root property to solve the equation. - $x ^ { 2 } = 112$