Question 1

Use the quadratic formula to solve the equation.
-$2 x ^ { 2 } + 12 x = - 5$

Accepted Answer

A)  $\frac { - 6 - \sqrt { 46 } } { 2 } , \frac { - 6 + \sqrt { 46 } } { 2 }$ 
B)  $\frac { - 12 - \sqrt { 26 } } { 2 } , \frac { - 12 + \sqrt { 26 } } { 2 }$ 
C)  $\frac { - 6 - \sqrt { 26 } } { 4 } , \frac { - 6 + \sqrt { 26 } } { 4 }$ 
D)  $\frac { - 6 - \sqrt { 26 } } { 2 } , \frac { - 6 + \sqrt { 26 } } { 2 }$ 
A)  $\frac { - 6 - \sqrt { 46 } } { 2 } , \frac { - 6 + \sqrt { 46 } } { 2 }$ 
B)  $\frac { - 12 - \sqrt { 26 } } { 2 } , \frac { - 12 + \sqrt { 26 } } { 2 }$ 
C)  $\frac { - 6 - \sqrt { 26 } } { 4 } , \frac { - 6 + \sqrt { 26 } } { 4 }$ 
D)  $\frac { - 6 - \sqrt { 26 } } { 2 } , \frac { - 6 + \sqrt { 26 } } { 2 }$

Question 2

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$\frac { ( x - 3 ) ^ { 2 } } { x ^ { 2 } - 25 } > 0$

Accepted Answer

A)  $( - 5,3 ) \cup ( 5 , \infty )$
  
B)  $( - \infty , - 5 ) \cup ( 5 , \infty )$
  
C)  $( - 5,3 ) \cup ( 3,5 )$
  
D)  $( - \infty , - 5 ) \cup ( 3,5 )$
  
A)  $( - 5,3 ) \cup ( 5 , \infty )$
  
B)  $( - \infty , - 5 ) \cup ( 5 , \infty )$
  
C)  $( - 5,3 ) \cup ( 3,5 )$
  
D)  $( - \infty , - 5 ) \cup ( 3,5 )$

Question 3

Write the equation of the parabola that has the same shape as the given parabola but with the given vertex.
-$f ( x ) = - 3 x ^ { 2 } ; ( 3 , - 4 )$

Accepted Answer

A)  $f ( x ) = - 3 ( x + 4 ) ^ { 2 } + 3$ 
B)  $f ( x ) = - 3 ( x - 4 ) ^ { 2 } + 3$ 
C)  $f ( x ) = - 3 ( x - 3 ) ^ { 2 } - 4$ 
D)  $f ( x ) = - 3 ( x + 3 ) ^ { 2 } - 4$ 
A)  $f ( x ) = - 3 ( x + 4 ) ^ { 2 } + 3$ 
B)  $f ( x ) = - 3 ( x - 4 ) ^ { 2 } + 3$ 
C)  $f ( x ) = - 3 ( x - 3 ) ^ { 2 } - 4$ 
D)  $f ( x ) = - 3 ( x + 3 ) ^ { 2 } - 4$

Question 4

Solve the equation.
-$( x + 5 ) ^ { 2 } = 14$

Accepted Answer

A)  $- \sqrt { 14 } , \sqrt { 14 }$ 
B)  $- 5 - \sqrt { 14 } , - 5 + \sqrt { 14 }$ 
C)  9 
D)  $5 - \sqrt { 14 } , 5 + \sqrt { 14 }$ 
A)  $- \sqrt { 14 } , \sqrt { 14 }$ 
B)  $- 5 - \sqrt { 14 } , - 5 + \sqrt { 14 }$ 
C)  9 
D)  $5 - \sqrt { 14 } , 5 + \sqrt { 14 }$

Question 5

Find the vertex of the graph of the quadratic function.
-$f ( x ) = - 6 x ^ { 2 } + 12 x + 9$

Accepted Answer

A)  $( 1,15 )$ 
B)  $( - 2 , - 39 )$ 
C)  $( 2 , - 3 )$ 
D)  $( - 1 , - 9 )$ 
A)  $( 1,15 )$ 
B)  $( - 2 , - 39 )$ 
C)  $( 2 , - 3 )$ 
D)  $( - 1 , - 9 )$

Question 6

Solve the equation by completing the square.
-$16 a ^ { 2 } + 1 = 3 a$

Accepted Answer

A)  $\frac { - 3 - i \sqrt { 55 } } { 32 } , \frac { 3 + i \sqrt { 55 } } { 32 }$ 
B)  $\frac { - 3 - i \sqrt { 55 } } { 32 } , \frac { - 3 + i \sqrt { 55 } } { 32 }$ 
C)  $\frac { 3 - i \sqrt { 55 } } { 32 } , \frac { 3 + i \sqrt { 55 } } { 32 }$ 
D)  $\frac { 3 - i \sqrt { 55 } } { 32 } , \frac { - 3 + i \sqrt { 55 } } { 32 }$ 
A)  $\frac { - 3 - i \sqrt { 55 } } { 32 } , \frac { 3 + i \sqrt { 55 } } { 32 }$ 
B)  $\frac { - 3 - i \sqrt { 55 } } { 32 } , \frac { - 3 + i \sqrt { 55 } } { 32 }$ 
C)  $\frac { 3 - i \sqrt { 55 } } { 32 } , \frac { 3 + i \sqrt { 55 } } { 32 }$ 
D)  $\frac { 3 - i \sqrt { 55 } } { 32 } , \frac { - 3 + i \sqrt { 55 } } { 32 }$

Question 7

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

Accepted Answer

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

Question 8

Solve.
-$x = 8 + 2 \sqrt { x }$

Accepted Answer

A)  16 
B)  32 
C)  8 
D)  12 
A)  16 
B)  32 
C)  8 
D)  12

Question 9

Solve the inequality. Write the solution set in interval notation.
-$\left( x ^ { 2 } - 64 \right) \left( x ^ { 2 } - 1 \right) > 0$

Accepted Answer

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

Question 10

Solve.
-A ball is thrown downward with an initial velocity of 28 meters per second from a cliff that is 60 meters high. The height of the ball is given by the quadratic equation $h = - 4.9 t ^ { 2 } - 28 t + 120$ where $\mathrm { h }$ is in meters and $\mathrm { t }$ is the time in seconds since the ball was thrown. Find the time that the ball will be 60 meters from the ground. Round your answer to the nearest tenth of a second.

Accepted Answer

A)  $2.7 \mathrm { sec }$ 
B)  $1.7 \mathrm { sec }$ 
C)  $1.8 \mathrm { sec }$ 
D)  $1.6 \mathrm { sec }$ 
A)  $2.7 \mathrm { sec }$ 
B)  $1.7 \mathrm { sec }$ 
C)  $1.8 \mathrm { sec }$ 
D)  $1.6 \mathrm { sec }$

Question 11

Use the quadratic formula to solve the equation.
-$x ^ { 2 } - 22 x + 121 = 0$

Accepted Answer

A)  $- 11 - i , - 11 + i$ 
B)  11 
C)  $- 11$ 
D)  $- 11,11$ 
A)  $- 11 - i , - 11 + i$ 
B)  11 
C)  $- 11$ 
D)  $- 11,11$

Question 12

Use the discriminant to determine the number and type of solutions of the equation.
-$x ^ { 2 } - 2 x + 1 = 0$

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 13

Solve.
-$2 + \frac { 5 } { 4 x - 1 } = - \frac { 2 } { ( 4 x - 1 ) ^ { 2 } }$

Accepted Answer

A)  $- \frac { 1 } { 4 } , \frac { 1 } { 8 }$ 
B)  $- \frac { 1 } { 4 } , - \frac { 1 } { 8 }$ 
C)  $- 2 , - \frac { 1 } { 2 }$ 
D)  $- \frac { 1 } { 4 } , 0$ 
A)  $- \frac { 1 } { 4 } , \frac { 1 } { 8 }$ 
B)  $- \frac { 1 } { 4 } , - \frac { 1 } { 8 }$ 
C)  $- 2 , - \frac { 1 } { 2 }$ 
D)  $- \frac { 1 } { 4 } , 0$

Question 14

Use the quadratic formula to solve the equation.
-$( x - 9 ) ( x - 1 ) = 14$

Accepted Answer

A)  $5 - 2 \sqrt { 5 } , 5 + 2 \sqrt { 5 }$ 
B)  $5 - \sqrt { 30 } , 5 + \sqrt { 30 }$ 
C)  $- 5 - \sqrt { 30 } , - 5 + \sqrt { 30 }$ 
D)  $- 5 - 2 \sqrt { 5 } , - 5 + 2 \sqrt { 5 }$ 
A)  $5 - 2 \sqrt { 5 } , 5 + 2 \sqrt { 5 }$ 
B)  $5 - \sqrt { 30 } , 5 + \sqrt { 30 }$ 
C)  $- 5 - \sqrt { 30 } , - 5 + \sqrt { 30 }$ 
D)  $- 5 - 2 \sqrt { 5 } , - 5 + 2 \sqrt { 5 }$

Question 15

Solve.
-A common equation used in business is a demand equation. It expresses the relationship between the unit price of some commodity and the quantity demanded. In the demand equation $p = - x ^ { 2 } + 108$, for a certain style of calculator, $p$ is the price per calculator in dollars and $x$ is the quantity demanded in thousands. Find the demand for the calculator if the price is $\$ 8$ per calculator.

Accepted Answer

A)  44 thousand units 
B)  11 thousand units 
C)  50 thousand units 
D)  10 thousand units 
A)  44 thousand units 
B)  11 thousand units 
C)  50 thousand units 
D)  10 thousand units

Question 16

Use the quadratic formula to solve the equation.
-$5 x ^ { 2 } = - 12 x - 2$

Accepted Answer

A)  $\frac { - 6 - \sqrt { 26 } } { 10 } , \frac { - 6 + \sqrt { 26 } } { 10 }$ 
B)  $\frac { - 6 - \sqrt { 26 } } { 5 } , \frac { - 6 + \sqrt { 26 } } { 5 }$ 
C)  $\frac { - 12 - \sqrt { 26 } } { 5 } , \frac { - 12 + \sqrt { 26 } } { 5 }$ 
D)  $\frac { - 6 - \sqrt { 46 } } { 5 } , \frac { - 6 + \sqrt { 46 } } { 5 }$ 
A)  $\frac { - 6 - \sqrt { 26 } } { 10 } , \frac { - 6 + \sqrt { 26 } } { 10 }$ 
B)  $\frac { - 6 - \sqrt { 26 } } { 5 } , \frac { - 6 + \sqrt { 26 } } { 5 }$ 
C)  $\frac { - 12 - \sqrt { 26 } } { 5 } , \frac { - 12 + \sqrt { 26 } } { 5 }$ 
D)  $\frac { - 6 - \sqrt { 46 } } { 5 } , \frac { - 6 + \sqrt { 46 } } { 5 }$

Question 17

Use the quadratic formula to solve the equation.
-$6 x ^ { 2 } + 22 x = - 18$

Accepted Answer

A)  $\frac { - 11 - \sqrt { 13 } } { 12 } , \frac { - 11 + \sqrt { 13 } } { 12 }$ 
B)  $\frac { - 11 - \sqrt { 229 } } { 6 } , \frac { - 11 + \sqrt { 229 } } { 6 }$ 
C)  $\frac { - 22 - \sqrt { 13 } } { 6 } , \frac { - 22 + \sqrt { 13 } } { 6 }$ 
D)  $\frac { - 11 - \sqrt { 13 } } { 6 } , \frac { - 11 + \sqrt { 13 } } { 6 }$ 
A)  $\frac { - 11 - \sqrt { 13 } } { 12 } , \frac { - 11 + \sqrt { 13 } } { 12 }$ 
B)  $\frac { - 11 - \sqrt { 229 } } { 6 } , \frac { - 11 + \sqrt { 229 } } { 6 }$ 
C)  $\frac { - 22 - \sqrt { 13 } } { 6 } , \frac { - 22 + \sqrt { 13 } } { 6 }$ 
D)  $\frac { - 11 - \sqrt { 13 } } { 6 } , \frac { - 11 + \sqrt { 13 } } { 6 }$

Question 18

Find all numbers that satisfy the following.
-An arrow is fired straight up from the ground with an initial velocity of 96 feet per second. Its height, $s ( t )$, in feet at any time $t$ is given by the function $s ( t ) = - 16 t ^ { 2 } + 96 t$. Find the interval of time for which the height of the arrow is less than 80 feet.

Accepted Answer

A)  after $5 \mathrm { sec }$ 
B)  between 1 and $5 \mathrm { sec }$ 
C)  before $1 \mathrm { sec }$ 
D)  before $1 \mathrm { sec }$ or after $5 \mathrm { sec }$ 
A)  after $5 \mathrm { sec }$ 
B)  between 1 and $5 \mathrm { sec }$ 
C)  before $1 \mathrm { sec }$ 
D)  before $1 \mathrm { sec }$ or after $5 \mathrm { sec }$

Question 19

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$x ^ { 2 } + 5 x \leq - 6$

Accepted Answer

A)  $( 2,3 )$
  
B)  $[ 2,3 ]$
  
C) $(-\infty, 2] \cup[3, \infty)$
  
D)  $[ - 3 , - 2 ]$
  
A)  $( 2,3 )$
  
B)  $[ 2,3 ]$
  
C) $(-\infty, 2] \cup[3, \infty)$
  
D)  $[ - 3 , - 2 ]$

Question 20

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

Accepted Answer

A)  $( - \infty , - 7 ) \cup ( 0 , \infty )$
  
B)  $( - \infty , 4 ) \cup ( 7 , \infty )$
  
C)  $( - 7 , - 4 ) \cup ( 0 , \infty )$
  
D)  $( - \infty , - 7 ) \cup ( - 4,0 )$
 
- 
A)  $( - \infty , - 7 ) \cup ( 0 , \infty )$
  
B)  $( - \infty , 4 ) \cup ( 7 , \infty )$
  
C)  $( - 7 , - 4 ) \cup ( 0 , \infty )$
  
D)  $( - \infty , - 7 ) \cup ( - 4,0 )$
 
-

Use the quadratic formula to solve the equation. - $2 x ^ { 2 } + 12 x = - 5$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $\frac { ( x - 3 ) ^ { 2 } } { x ^ { 2 } - 25 } > 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - \frac { ( x - 3 ) ^ { 2 } } { x ^ { 2 } - 25 } > 0$

Write the equation of the parabola that has the same shape as the given parabola but with the given vertex. - $f ( x ) = - 3 x ^ { 2 } ; ( 3 , - 4 )$

Solve the equation. - $( x + 5 ) ^ { 2 } = 14$

Find the vertex of the graph of the quadratic function. - $f ( x ) = - 6 x ^ { 2 } + 12 x + 9$

Solve the equation by completing the square. - $16 a ^ { 2 } + 1 = 3 a$

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

Solve. - $x = 8 + 2 \sqrt { x }$

Solve the inequality. Write the solution set in interval notation. - $\left( x ^ { 2 } - 64 \right) \left( x ^ { 2 } - 1 \right) > 0$

Use the quadratic formula to solve the equation. - $x ^ { 2 } - 22 x + 121 = 0$

Use the discriminant to determine the number and type of solutions of the equation. - $x ^ { 2 } - 2 x + 1 = 0$

Solve. - $2 + \frac { 5 } { 4 x - 1 } = - \frac { 2 } { ( 4 x - 1 ) ^ { 2 } }$

Use the quadratic formula to solve the equation. - $( x - 9 ) ( x - 1 ) = 14$

Use the quadratic formula to solve the equation. - $5 x ^ { 2 } = - 12 x - 2$

Use the quadratic formula to solve the equation. - $6 x ^ { 2 } + 22 x = - 18$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $x ^ { 2 } + 5 x \leq - 6$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - x ^ { 2 } + 5 x \leq - 6$

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

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

Use the quadratic formula to solve the equation. - 2x2+12x=−52 x ^ { 2 } + 12 x = - 52x2+12x=−5

Solve the inequality. Graph the solution set and write the solution set in interval notation. - (x−3)2x2−25>0\frac { ( x - 3 ) ^ { 2 } } { x ^ { 2 } - 25 } > 0x2−25(x−3)2​>0

Write the equation of the parabola that has the same shape as the given parabola but with the given vertex. - f(x)=−3x2;(3,−4)f ( x ) = - 3 x ^ { 2 } ; ( 3 , - 4 )f(x)=−3x2;(3,−4)

Solve the equation. - (x+5)2=14( x + 5 ) ^ { 2 } = 14(x+5)2=14

Find the vertex of the graph of the quadratic function. - f(x)=−6x2+12x+9f ( x ) = - 6 x ^ { 2 } + 12 x + 9f(x)=−6x2+12x+9

Solve the equation by completing the square. - 16a2+1=3a16 a ^ { 2 } + 1 = 3 a16a2+1=3a

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

Solve. - x=8+2xx = 8 + 2 \sqrt { x }x=8+2x​

Solve the inequality. Write the solution set in interval notation. - (x2−64)(x2−1)>0\left( x ^ { 2 } - 64 \right) \left( x ^ { 2 } - 1 \right) > 0(x2−64)(x2−1)>0

Use the quadratic formula to solve the equation. - x2−22x+121=0x ^ { 2 } - 22 x + 121 = 0x2−22x+121=0

Use the discriminant to determine the number and type of solutions of the equation. - x2−2x+1=0x ^ { 2 } - 2 x + 1 = 0x2−2x+1=0

Solve. - 2+54x−1=−2(4x−1)22 + \frac { 5 } { 4 x - 1 } = - \frac { 2 } { ( 4 x - 1 ) ^ { 2 } }2+4x−15​=−(4x−1)22​

Use the quadratic formula to solve the equation. - (x−9)(x−1)=14( x - 9 ) ( x - 1 ) = 14(x−9)(x−1)=14

Use the quadratic formula to solve the equation. - 5x2=−12x−25 x ^ { 2 } = - 12 x - 25x2=−12x−2

Use the quadratic formula to solve the equation. - 6x2+22x=−186 x ^ { 2 } + 22 x = - 186x2+22x=−18

Solve the inequality. Graph the solution set and write the solution set in interval notation. - x2+5x≤−6x ^ { 2 } + 5 x \leq - 6x2+5x≤−6

Solve the inequality. Graph the solution set and write the solution set in interval notation. - 3xx+7<x\frac { 3 x } { x + 7 } < xx+73x​<x