Question 1

Solve.
-$5 x ^ { 4 } - 403 x ^ { 2 } - 162 = 0$

Accepted Answer

A)  $- 9,9 , - \frac { \mathrm { i } \sqrt { 10 } } { 5 } , \frac { \mathrm { i } \sqrt { 10 } } { 5 }$ 
B)  $9 , \frac { \mathrm { i } \sqrt { 10 } } { 5 }$ 
C)  $- 9 i , 9 i , - \frac { i \sqrt { 10 } } { 5 } , \frac { i \sqrt { 10 } } { 5 }$ 
D)  $- \frac { \sqrt { 10 } } { 5 } , \frac { \sqrt { 10 } } { 5 } , - 9,9$ 
A)  $- 9,9 , - \frac { \mathrm { i } \sqrt { 10 } } { 5 } , \frac { \mathrm { i } \sqrt { 10 } } { 5 }$ 
B)  $9 , \frac { \mathrm { i } \sqrt { 10 } } { 5 }$ 
C)  $- 9 i , 9 i , - \frac { i \sqrt { 10 } } { 5 } , \frac { i \sqrt { 10 } } { 5 }$ 
D)  $- \frac { \sqrt { 10 } } { 5 } , \frac { \sqrt { 10 } } { 5 } , - 9,9$

Question 2

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

Accepted Answer

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

Question 3

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$4 x ^ { 2 } - 3 x \geq 7$

Accepted Answer

A)  $\left( - 1 , \frac { 7 } { 4 } \right)$
  
B)  $( - \infty , - 1 ) \cup \left( \frac { 7 } { 4 } , \infty \right)$
  
C)  $\left[ - 1 , \frac { 7 } { 4 } \right]$
  
D)  $( - \infty , - 1 ] \cup \left[ \frac { 7 } { 4 } , \infty \right)$
  
A)  $\left( - 1 , \frac { 7 } { 4 } \right)$
  
B)  $( - \infty , - 1 ) \cup \left( \frac { 7 } { 4 } , \infty \right)$
  
C)  $\left[ - 1 , \frac { 7 } { 4 } \right]$
  
D)  $( - \infty , - 1 ] \cup \left[ \frac { 7 } { 4 } , \infty \right)$

Question 4

Solve the equation.
-$x ^ { 6 } + 49 = 49 x ^ { 4 } + x ^ { 2 }$

Accepted Answer

A)  $- 7,7 , - i , i$ 
B)  $- 7,7 , - 1,1 , - 7 i , 7 i$ 
C)  $- 7,7 , - 1,1$ 
D)  $- 7,7 , - 1,1 , - \mathrm { i } , \mathrm { i }$ 
A)  $- 7,7 , - i , i$ 
B)  $- 7,7 , - 1,1 , - 7 i , 7 i$ 
C)  $- 7,7 , - 1,1$ 
D)  $- 7,7 , - 1,1 , - \mathrm { i } , \mathrm { i }$

Question 5

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$( 3 x - 1 ) ( x + 6 ) \leq 0$

Accepted Answer

A)  $\left[ - \infty , \frac { 1 } { 3 } \right]$
  
B)  $[ - 6 , \infty )$
  
C)  $\left[ - 6 , \frac { 1 } { 3 } \right]$
  
D)  $( - \infty , - 6 ] \cup \left[ \frac { 1 } { 3 } , \infty \right]$
  
A)  $\left[ - \infty , \frac { 1 } { 3 } \right]$
  
B)  $[ - 6 , \infty )$
  
C)  $\left[ - 6 , \frac { 1 } { 3 } \right]$
  
D)  $( - \infty , - 6 ] \cup \left[ \frac { 1 } { 3 } , \infty \right]$

Question 6

Solve the equation by completing the square.
-$x ^ { 2 } + 12 x + 32 = 0$

Accepted Answer

A)  $\sqrt { 2 } , - 1$ 
B)  $- 4 , - 8$ 
C)  4,8 
D)  $40 , - 8$ 
A)  $\sqrt { 2 } , - 1$ 
B)  $- 4 , - 8$ 
C)  4,8 
D)  $40 , - 8$

Question 7

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$( 3 z + 4 ) ( 2 z - 7 ) \leq 0$

Accepted Answer

A)  $\left( - \infty , - \frac { 4 } { 3 } \right] \cup \left[ \frac { 7 } { 2 } , \infty \right)$
  
B)  $\left[ - \frac { 4 } { 3 } , \frac { 7 } { 2 } \right]$
  
C)  $\left( - \infty , - \frac { 4 } { 3 } \right) \cup \left( \frac { 7 } { 2 } , \infty \right)$
  
D)  $\left( - \frac { 4 } { 3 } , \frac { 7 } { 2 } \right)$
  
A)  $\left( - \infty , - \frac { 4 } { 3 } \right] \cup \left[ \frac { 7 } { 2 } , \infty \right)$
  
B)  $\left[ - \frac { 4 } { 3 } , \frac { 7 } { 2 } \right]$
  
C)  $\left( - \infty , - \frac { 4 } { 3 } \right) \cup \left( \frac { 7 } { 2 } , \infty \right)$
  
D)  $\left( - \frac { 4 } { 3 } , \frac { 7 } { 2 } \right)$

Question 8

Solve the equation by completing the square.
-$25 x ^ { 2 } + 60 x + 27 = 0$

Accepted Answer

A)  $\frac { 3 } { 5 } , \frac { 9 } { 5 }$ 
B)  $- \frac { 3 } { 5 } , - \frac { 9 } { 5 }$ 
C)  $- \frac { 9 } { 25 } , \frac { 36 } { 25 }$ 
D)  $- \frac { 3 } { 25 } , - \frac { 9 } { 25 }$ 
A)  $\frac { 3 } { 5 } , \frac { 9 } { 5 }$ 
B)  $- \frac { 3 } { 5 } , - \frac { 9 } { 5 }$ 
C)  $- \frac { 9 } { 25 } , \frac { 36 } { 25 }$ 
D)  $- \frac { 3 } { 25 } , - \frac { 9 } { 25 }$

Question 9

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

Accepted Answer

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

Question 10

Find all numbers that satisfy the following.
-The total profit function $\mathrm { P } ( \mathrm { x } )$ for a company producing $x$ thousand units is given by $P ( x ) = - 3 x ^ { 2 } + 45 x - 162$. Find the values of $x$ for which the company makes a profit. [Hint: The company makes a profit when $\mathrm { P } ( \mathrm { x } ) > 0$.]

Accepted Answer

A)  $x$ is greater than 6 thousand units 
B)  $x$ is less than 9 thousand units 
C)  $x$ is between 6 thousand units and 9 thousand units 
D)  $x$ is less than 6 thousand units or greater than 9 thousand units 
A)  $x$ is greater than 6 thousand units 
B)  $x$ is less than 9 thousand units 
C)  $x$ is between 6 thousand units and 9 thousand units 
D)  $x$ is less than 6 thousand units or greater than 9 thousand units

Question 11

Solve.
-$( 3 x - 6 ) ^ { 2 } - 4 ( 3 x - 6 ) - 5 = 0$

Accepted Answer

A)  $- \frac { 11 } { 3 } , - \frac { 5 } { 3 }$ 
B)  $- \frac { 1 } { 6 } , \frac { 7 } { 3 }$ 
C)  $\frac { 11 } { 3 } , \frac { 5 } { 3 }$ 
D)  $\frac { 1 } { 3 } , - \frac { 7 } { 3 }$ 
A)  $- \frac { 11 } { 3 } , - \frac { 5 } { 3 }$ 
B)  $- \frac { 1 } { 6 } , \frac { 7 } { 3 }$ 
C)  $\frac { 11 } { 3 } , \frac { 5 } { 3 }$ 
D)  $\frac { 1 } { 3 } , - \frac { 7 } { 3 }$

Question 12

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$x ( x + 4 ) ( x - 6 ) \leq 0$

Accepted Answer

A) $(-\infty,-4) \cup(0,6)$
  
B)  $( - 4,0 ) \cup ( 6 , \infty )$
  
C) $[ - 4,0 ] \cup [ 6 , \infty )$
  
D)  $( - \infty , - 4 ] \cup [ 0,6 ]$
  
A) $(-\infty,-4) \cup(0,6)$
  
B)  $( - 4,0 ) \cup ( 6 , \infty )$
  
C) $[ - 4,0 ] \cup [ 6 , \infty )$
  
D)  $( - \infty , - 4 ] \cup [ 0,6 ]$

Question 13

Use the square root property to solve the equation.
-$x ^ { 2 } - 22 = 0$

Accepted Answer

A)  11 
B)  $\sqrt { 22 }$ 
C)  484 
D)  $- \sqrt { 22 } , \sqrt { 22 }$ 
A)  11 
B)  $\sqrt { 22 }$ 
C)  484 
D)  $- \sqrt { 22 } , \sqrt { 22 }$

Question 14

Solve.
-$\frac { 9 } { x - 7 } + \frac { x } { x + 7 } = \frac { 72 } { x ^ { 2 } - 49 }$

Accepted Answer

A)  $- 1 - 2 \mathrm { i } \sqrt { 2 } , - 1 + 2 \mathrm { i } \sqrt { 2 }$ 
B)  $- 1 - \sqrt { 10 } , - 1 + \sqrt { 10 }$ 
C)  $1 - 2 i \sqrt { 2 } , 1 + 2 i \sqrt { 2 }$ 
D)  $1 - \sqrt { 10 } , 1 + \sqrt { 10 }$ 
A)  $- 1 - 2 \mathrm { i } \sqrt { 2 } , - 1 + 2 \mathrm { i } \sqrt { 2 }$ 
B)  $- 1 - \sqrt { 10 } , - 1 + \sqrt { 10 }$ 
C)  $1 - 2 i \sqrt { 2 } , 1 + 2 i \sqrt { 2 }$ 
D)  $1 - \sqrt { 10 } , 1 + \sqrt { 10 }$

Question 15

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 1600 feet high.

Accepted Answer

A)  $100 \mathrm { sec }$ 
B)  $9 \mathrm { sec }$ 
C)  $11 \mathrm { sec }$ 
D)  $10 \mathrm { sec }$ 
A)  $100 \mathrm { sec }$ 
B)  $9 \mathrm { sec }$ 
C)  $11 \mathrm { sec }$ 
D)  $10 \mathrm { sec }$

Question 16

Use the square root property to solve the equation.
-$( x - 6 ) ^ { 2 } = 49$

Accepted Answer

A)  $13 , - 1$ 
B)  $7 , - 7$ 
C)  $- 1 , - 13$ 
D)  55 
A)  $13 , - 1$ 
B)  $7 , - 7$ 
C)  $- 1 , - 13$ 
D)  55

Question 17

Solve.
-A ball is thrown upward with an initial velocity of 35 meters per second from a cliff that is 90 meters high. The height of the ball is given by the quadratic equation $h = - 4.9 t ^ { 2 } + 35 t + 90$ where $h$ is in meters and $t$ 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)  $9.2 \mathrm { sec }$ 
B)  $9.7 \mathrm { sec }$ 
C)  $14.2 \mathrm { sec }$ 
D)  $8.7 \mathrm { sec }$ 
A)  $9.2 \mathrm { sec }$ 
B)  $9.7 \mathrm { sec }$ 
C)  $14.2 \mathrm { sec }$ 
D)  $8.7 \mathrm { sec }$

Question 18

Given the accompanying graph of y = f(x), sketch the graph of the following.
-$y = f ( x + 2 ) + 1$
 
$y = f ( x )$

Accepted Answer

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

Question 19

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$\frac { ( x + 8 ) ( x - 4 ) } { x - 1 } \geq 0$

Accepted Answer

A) $[-8,1) \cup(1,4]$
  
B) $[-8,1) \cup[4, \infty)$
  
C)  $( - \infty , - 8 ] \cup ( 1,4 ]$
  
D)  $( - \infty , - 8 ] \cup [ 4 , \infty )$
  
A) $[-8,1) \cup(1,4]$
  
B) $[-8,1) \cup[4, \infty)$
  
C)  $( - \infty , - 8 ] \cup ( 1,4 ]$
  
D)  $( - \infty , - 8 ] \cup [ 4 , \infty )$

Question 20

Sketch the graph of the quadratic function by finding the vertex, intercepts, and determining if the graph opens upward
or downward.
-$f(x)=x^{2}+6 x$

Accepted Answer

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

Solve. - $5 x ^ { 4 } - 403 x ^ { 2 } - 162 = 0$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $4 x ^ { 2 } - 3 x \geq 7$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - 4 x ^ { 2 } - 3 x \geq 7$

Solve the equation. - $x ^ { 6 } + 49 = 49 x ^ { 4 } + x ^ { 2 }$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $( 3 x - 1 ) ( x + 6 ) \leq 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - ( 3 x - 1 ) ( x + 6 ) \leq 0$

Solve the equation by completing the square. - $x ^ { 2 } + 12 x + 32 = 0$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $( 3 z + 4 ) ( 2 z - 7 ) \leq 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - ( 3 z + 4 ) ( 2 z - 7 ) \leq 0$

Solve the equation by completing the square. - $25 x ^ { 2 } + 60 x + 27 = 0$

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

Solve. - $( 3 x - 6 ) ^ { 2 } - 4 ( 3 x - 6 ) - 5 = 0$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $x ( x + 4 ) ( x - 6 ) \leq 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - x ( x + 4 ) ( x - 6 ) \leq 0$

Use the square root property to solve the equation. - $x ^ { 2 } - 22 = 0$

Solve. - $\frac { 9 } { x - 7 } + \frac { x } { x + 7 } = \frac { 72 } { x ^ { 2 } - 49 }$

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 1600 feet high.

Use the square root property to solve the equation. - $( x - 6 ) ^ { 2 } = 49$

Given the accompanying graph of y = f(x), sketch the graph of the following. - $y = f ( x + 2 ) + 1$ $y = f ( x )$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $\frac { ( x + 8 ) ( x - 4 ) } { x - 1 } \geq 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - \frac { ( x + 8 ) ( x - 4 ) } { x - 1 } \geq 0$

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

Solve. - 5x4−403x2−162=05 x ^ { 4 } - 403 x ^ { 2 } - 162 = 05x4−403x2−162=0

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

Solve the inequality. Graph the solution set and write the solution set in interval notation. - 4x2−3x≥74 x ^ { 2 } - 3 x \geq 74x2−3x≥7

Solve the equation. - x6+49=49x4+x2x ^ { 6 } + 49 = 49 x ^ { 4 } + x ^ { 2 }x6+49=49x4+x2

Solve the inequality. Graph the solution set and write the solution set in interval notation. - (3x−1)(x+6)≤0( 3 x - 1 ) ( x + 6 ) \leq 0(3x−1)(x+6)≤0

Solve the equation by completing the square. - x2+12x+32=0x ^ { 2 } + 12 x + 32 = 0x2+12x+32=0

Solve the inequality. Graph the solution set and write the solution set in interval notation. - (3z+4)(2z−7)≤0( 3 z + 4 ) ( 2 z - 7 ) \leq 0(3z+4)(2z−7)≤0

Solve the equation by completing the square. - 25x2+60x+27=025 x ^ { 2 } + 60 x + 27 = 025x2+60x+27=0

Solve the equation by completing the square. - x2+10x=−6x ^ { 2 } + 10 x = - 6x2+10x=−6

Solve. - (3x−6)2−4(3x−6)−5=0( 3 x - 6 ) ^ { 2 } - 4 ( 3 x - 6 ) - 5 = 0(3x−6)2−4(3x−6)−5=0

Solve the inequality. Graph the solution set and write the solution set in interval notation. - x(x+4)(x−6)≤0x ( x + 4 ) ( x - 6 ) \leq 0x(x+4)(x−6)≤0

Use the square root property to solve the equation. - x2−22=0x ^ { 2 } - 22 = 0x2−22=0

Solve. - 9x−7+xx+7=72x2−49\frac { 9 } { x - 7 } + \frac { x } { x + 7 } = \frac { 72 } { x ^ { 2 } - 49 }x−79​+x+7x​=x2−4972​

Use the square root property to solve the equation. - (x−6)2=49( x - 6 ) ^ { 2 } = 49(x−6)2=49

Given the accompanying graph of y = f(x), sketch the graph of the following. - y=f(x+2)+1y = f ( x + 2 ) + 1y=f(x+2)+1 y=f(x)y = f ( x )y=f(x)

Solve the inequality. Graph the solution set and write the solution set in interval notation. - (x+8)(x−4)x−1≥0\frac { ( x + 8 ) ( x - 4 ) } { x - 1 } \geq 0x−1(x+8)(x−4)​≥0

Sketch the graph of the quadratic function by finding the vertex, intercepts, and determining if the graph opens upward or downward. - f(x)=x2+6xf(x)=x^{2}+6 xf(x)=x2+6x

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

Solve. - $5 x ^ { 4 } - 403 x ^ { 2 } - 162 = 0$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $4 x ^ { 2 } - 3 x \geq 7$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - 4 x ^ { 2 } - 3 x \geq 7$

Solve the equation. - $x ^ { 6 } + 49 = 49 x ^ { 4 } + x ^ { 2 }$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $( 3 x - 1 ) ( x + 6 ) \leq 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - ( 3 x - 1 ) ( x + 6 ) \leq 0$

Solve the equation by completing the square. - $x ^ { 2 } + 12 x + 32 = 0$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $( 3 z + 4 ) ( 2 z - 7 ) \leq 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - ( 3 z + 4 ) ( 2 z - 7 ) \leq 0$

Solve the equation by completing the square. - $25 x ^ { 2 } + 60 x + 27 = 0$

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

Solve. - $( 3 x - 6 ) ^ { 2 } - 4 ( 3 x - 6 ) - 5 = 0$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $x ( x + 4 ) ( x - 6 ) \leq 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - x ( x + 4 ) ( x - 6 ) \leq 0$

Use the square root property to solve the equation. - $x ^ { 2 } - 22 = 0$

Solve. - $\frac { 9 } { x - 7 } + \frac { x } { x + 7 } = \frac { 72 } { x ^ { 2 } - 49 }$

Use the square root property to solve the equation. - $( x - 6 ) ^ { 2 } = 49$

Given the accompanying graph of y = f(x), sketch the graph of the following. - $y = f ( x + 2 ) + 1$ $y = f ( x )$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $\frac { ( x + 8 ) ( x - 4 ) } { x - 1 } \geq 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - \frac { ( x + 8 ) ( x - 4 ) } { x - 1 } \geq 0$