Question 1

Write the equation of the parabola that has the same shape as the given parabola but with the given vertex.
-$f ( x ) = 5 x ^ { 2 } ; ( - 1,3 )$

Accepted Answer

A)  $f ( x ) = 5 ( x - 1 ) ^ { 2 } + 3$ 
B)  $f ( x ) = 5 ( x + 3 ) ^ { 2 } - 3$ 
C)  $f ( x ) = 5 ( x - 3 ) ^ { 2 } - 3$ 
D)  $f ( x ) = 5 ( x + 1 ) ^ { 2 } + 3$ 
A)  $f ( x ) = 5 ( x - 1 ) ^ { 2 } + 3$ 
B)  $f ( x ) = 5 ( x + 3 ) ^ { 2 } - 3$ 
C)  $f ( x ) = 5 ( x - 3 ) ^ { 2 } - 3$ 
D)  $f ( x ) = 5 ( x + 1 ) ^ { 2 } + 3$

Question 2

Use the quadratic formula to solve the equation.
-$x ( x - 10 ) = 3$

Accepted Answer

A)  $- 5 + 2 \sqrt { 7 } , - 5 - 2 \sqrt { 7 }$ 
B)  $5 - 2 \sqrt { 7 } , 5 + 2 \sqrt { 7 }$ 
C)  $5 - \sqrt { 22 } , 5 + \sqrt { 22 }$ 
D)  $- 5 + \sqrt { 22 } , - 5 - \sqrt { 22 }$ 
A)  $- 5 + 2 \sqrt { 7 } , - 5 - 2 \sqrt { 7 }$ 
B)  $5 - 2 \sqrt { 7 } , 5 + 2 \sqrt { 7 }$ 
C)  $5 - \sqrt { 22 } , 5 + \sqrt { 22 }$ 
D)  $- 5 + \sqrt { 22 } , - 5 - \sqrt { 22 }$

Question 3

Solve.
-An isosceles right triangle has legs of equal length. If the hypotenuse is 22 inches long, find the length of each leg.

Accepted Answer

A)  $11 \sqrt { 2 } \mathrm { in }$. 
B)  $121 \sqrt { 2 } \mathrm { in } .$ 
C)  $22 \sqrt { 2 } \mathrm { in }$. 
D)  $\frac { 11 } { 2 } \sqrt { 2 }$ in. 
A)  $11 \sqrt { 2 } \mathrm { in }$. 
B)  $121 \sqrt { 2 } \mathrm { in } .$ 
C)  $22 \sqrt { 2 } \mathrm { in }$. 
D)  $\frac { 11 } { 2 } \sqrt { 2 }$ in.

Question 4

Use the square root property to solve the equation.
-$( 5 x + 5 ) ^ { 2 } = 100$

Accepted Answer

A)  1,3 
B)  0,1 
C)  $21 , - 21$ 
D)  $1 , - 3$ 
A)  1,3 
B)  0,1 
C)  $21 , - 21$ 
D)  $1 , - 3$

Question 5

Use the quadratic formula to solve the equation.
-$4 x ^ { 2 } + 6 x + 1 = 0$

Accepted Answer

A)  $\frac { - 3 - \sqrt { 13 } } { 4 } , \frac { - 3 + \sqrt { 13 } } { 4 }$ 
B)  $\frac { - 3 - \sqrt { 5 } } { 4 } , \frac { - 3 + \sqrt { 5 } } { 4 }$ 
C)  $\frac { - 3 - \sqrt { 5 } } { 8 } , \frac { - 3 + \sqrt { 5 } } { 8 }$ 
D)  $\frac { - 6 - \sqrt { 5 } } { 4 } , \frac { - 6 + \sqrt { 5 } } { 4 }$ 
A)  $\frac { - 3 - \sqrt { 13 } } { 4 } , \frac { - 3 + \sqrt { 13 } } { 4 }$ 
B)  $\frac { - 3 - \sqrt { 5 } } { 4 } , \frac { - 3 + \sqrt { 5 } } { 4 }$ 
C)  $\frac { - 3 - \sqrt { 5 } } { 8 } , \frac { - 3 + \sqrt { 5 } } { 8 }$ 
D)  $\frac { - 6 - \sqrt { 5 } } { 4 } , \frac { - 6 + \sqrt { 5 } } { 4 }$

Question 6

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

Accepted Answer

A)  8 
B)  4 
C)  $- 4,4$ 
D)  $- 5,5$ 
A)  8 
B)  4 
C)  $- 4,4$ 
D)  $- 5,5$

Question 7

Write the equation of the parabola that has the same shape as the given parabola but with the given vertex.
-$f ( x ) = - 4 x ^ { 2 } ; ( 3,7 )$

Accepted Answer

A)  $f ( x ) = - 4 ( x - 7 ) ^ { 2 } - 3$ 
B)  $f ( x ) = - 4 ( x - 3 ) ^ { 2 } + 7$ 
C)  $f ( x ) = - 4 ( x + 3 ) ^ { 2 } + 7$ 
D)  $f ( x ) = - 4 ( x + 7 ) ^ { 2 } - 3$ 
A)  $f ( x ) = - 4 ( x - 7 ) ^ { 2 } - 3$ 
B)  $f ( x ) = - 4 ( x - 3 ) ^ { 2 } + 7$ 
C)  $f ( x ) = - 4 ( x + 3 ) ^ { 2 } + 7$ 
D)  $f ( x ) = - 4 ( x + 7 ) ^ { 2 } - 3$

Question 8

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
-$f(x)=-4(x+2)^{2}-5$

Accepted Answer

A)  vertex $( 5,2 )$; axis $x = 5$
  
B)  vertex $( - 5 , - 2 )$; axis $x = - 5$
  
C)  vertex $( 2 , - 5 )$; axis $x = 2$
  
D)  vertex $( - 2 , - 5 )$; axis $x = - 2$
  
A)  vertex $( 5,2 )$; axis $x = 5$
  
B)  vertex $( - 5 , - 2 )$; axis $x = - 5$
  
C)  vertex $( 2 , - 5 )$; axis $x = 2$
  
D)  vertex $( - 2 , - 5 )$; axis $x = - 2$

Question 9

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

Accepted Answer

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

Question 10

Use the quadratic formula to solve the equation.
-$\frac { x ^ { 2 } } { 16 } + x + \frac { 41 } { 16 } = 0$

Accepted Answer

A)  $8 - \sqrt { 41 } , 8 + \sqrt { 41 }$ 
B)  $8 + \sqrt { 23 }$ 
C)  $- 16 + \sqrt { 41 }$ 
D)  $- 8 - \sqrt { 23 } , - 8 + \sqrt { 23 }$ 
A)  $8 - \sqrt { 41 } , 8 + \sqrt { 41 }$ 
B)  $8 + \sqrt { 23 }$ 
C)  $- 16 + \sqrt { 41 }$ 
D)  $- 8 - \sqrt { 23 } , - 8 + \sqrt { 23 }$

Question 11

Use the quadratic formula to solve the equation.
-$16 x ^ { 2 } + 1 = 5 x$

Accepted Answer

A)  $\frac { 5 - i \sqrt { 39 } } { 32 } , \frac { - 5 + i \sqrt { 39 } } { 32 }$ 
B)  $\frac { 5 - i \sqrt { 39 } } { 32 } , \frac { 5 + i \sqrt { 39 } } { 32 }$ 
C)  $\frac { - 5 - i \sqrt { 39 } } { 32 } , \frac { - 5 + i \sqrt { 39 } } { 32 }$ 
D)  $\frac { - 5 - i \sqrt { 39 } } { 32 } , \frac { 5 + i \sqrt { 39 } } { 32 }$ 
A)  $\frac { 5 - i \sqrt { 39 } } { 32 } , \frac { - 5 + i \sqrt { 39 } } { 32 }$ 
B)  $\frac { 5 - i \sqrt { 39 } } { 32 } , \frac { 5 + i \sqrt { 39 } } { 32 }$ 
C)  $\frac { - 5 - i \sqrt { 39 } } { 32 } , \frac { - 5 + i \sqrt { 39 } } { 32 }$ 
D)  $\frac { - 5 - i \sqrt { 39 } } { 32 } , \frac { 5 + i \sqrt { 39 } } { 32 }$

Question 12

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l l } 
\text { quadratic formula } & \text { quadratic } & \text { discriminant } & \pm \sqrt { b } \
\text { completing the square } & \text { quadratic inequality } & ( h , k ) & ( 0 , k ) \
( h , 0 ) & \frac { - b } { 2 a } & &
\end{array}$$
-The ---------helps us find the number and type of solutions of a quadratic equation.

Accepted Answer

A)  quadratic 
B)  quadratic formula 
C)  discriminant 
D)  completing the square 
A)  quadratic 
B)  quadratic formula 
C)  discriminant 
D)  completing the square

Question 13

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 14

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

Accepted Answer

A)  $- 1 , - \mathrm { i } \sqrt { 3 } , \mathrm { i } \sqrt { 3 }$ 
B)  $1 , - \sqrt { 3 } , \sqrt { 3 }$ 
C)  $1 , - \mathrm { i } \sqrt { 3 } , \mathrm { i } \sqrt { 3 }$ 
D)  $- 1 , - \sqrt { 3 } , \sqrt { 3 }$ 
A)  $- 1 , - \mathrm { i } \sqrt { 3 } , \mathrm { i } \sqrt { 3 }$ 
B)  $1 , - \sqrt { 3 } , \sqrt { 3 }$ 
C)  $1 , - \mathrm { i } \sqrt { 3 } , \mathrm { i } \sqrt { 3 }$ 
D)  $- 1 , - \sqrt { 3 } , \sqrt { 3 }$

Question 15

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$x ^ { 2 } + 6 x - 7 \geq 0$

Accepted Answer

A)  $[ - 7,1 ]$
  
B)  $( - \infty , - 7 ]$
  
C) $[ 1 , \infty )$
  
D)  $( - \infty , - 7 ] \cup [ 1 , \infty )$
  
A)  $[ - 7,1 ]$
  
B)  $( - \infty , - 7 ]$
  
C) $[ 1 , \infty )$
  
D)  $( - \infty , - 7 ] \cup [ 1 , \infty )$

Question 16

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
-$x ^ { 2 } + \frac { 2 } { 11 } x +$____

Accepted Answer

A)  $x ^ { 2 } + \frac { 2 } { 11 } x + \frac { 2 } { 121 } = \left( x + \frac { 1 } { 11 } \right) ^ { 2 }$ 
B)  $x ^ { 2 } + \frac { 2 } { 11 } x + \frac { 1 } { \underline { 121 } } = \left( x + \frac { 1 } { 11 } \right) ^ { 2 }$ 
C)  $x ^ { 2 } + \frac { 2 } { 11 } x + \frac { 1 } { \underline { 11 } } = \left( x + \frac { 1 } { 121 } \right) ^ { 2 }$ 
D)  $x ^ { 2 } + \frac { 2 } { 11 } x + \frac { 4 } { 121 } = \left( x + \frac { 2 } { 11 } \right) ^ { 2 }$ 
A)  $x ^ { 2 } + \frac { 2 } { 11 } x + \frac { 2 } { 121 } = \left( x + \frac { 1 } { 11 } \right) ^ { 2 }$ 
B)  $x ^ { 2 } + \frac { 2 } { 11 } x + \frac { 1 } { \underline { 121 } } = \left( x + \frac { 1 } { 11 } \right) ^ { 2 }$ 
C)  $x ^ { 2 } + \frac { 2 } { 11 } x + \frac { 1 } { \underline { 11 } } = \left( x + \frac { 1 } { 121 } \right) ^ { 2 }$ 
D)  $x ^ { 2 } + \frac { 2 } { 11 } x + \frac { 4 } { 121 } = \left( x + \frac { 2 } { 11 } \right) ^ { 2 }$

Question 17

Use the discriminant to determine the number and type of solutions of the equation.
-$x ^ { 2 } - 3 x + 4 = 0$

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 18

Use the square root property to solve the equation.
-$x ^ { 2 } + 144 = 0$

Accepted Answer

A)  $- 12 \mathrm { i } , 12 \mathrm { i }$ 
B)  12 
C)  20,736 
D)  $- 12,12$ 
A)  $- 12 \mathrm { i } , 12 \mathrm { i }$ 
B)  12 
C)  20,736 
D)  $- 12,12$

Question 19

Solve the equation by completing the square.
-$x ^ { 2 } + 5 x - 5 = 0$

Accepted Answer

A)  $- 5 - 3 \sqrt { 5 } , - 5 + 3 \sqrt { 5 }$ 
B)  $\frac { 5 + 3 \sqrt { 5 } } { 2 }$ 
C)  $\frac { - 5 - 3 \sqrt { 5 } } { 2 } , \frac { - 5 + 3 \sqrt { 5 } } { 2 }$ 
D)  $\frac { - 5 - 3 \sqrt { 5 } } { 2 }$ 
A)  $- 5 - 3 \sqrt { 5 } , - 5 + 3 \sqrt { 5 }$ 
B)  $\frac { 5 + 3 \sqrt { 5 } } { 2 }$ 
C)  $\frac { - 5 - 3 \sqrt { 5 } } { 2 } , \frac { - 5 + 3 \sqrt { 5 } } { 2 }$ 
D)  $\frac { - 5 - 3 \sqrt { 5 } } { 2 }$

Question 20

Find the vertex of the graph of the quadratic function.
-$f ( x ) = - x ^ { 2 } + x - 4$

Accepted Answer

A)  $( 1 , - 4 )$ 
B)  $( - 1 , - 6 )$ 
C)  $\left( - \frac { 1 } { 2 } , - \frac { 19 } { 4 } \right)$ 
D)  $\left( \frac { 1 } { 2 } , - \frac { 15 } { 4 } \right)$ 
A)  $( 1 , - 4 )$ 
B)  $( - 1 , - 6 )$ 
C)  $\left( - \frac { 1 } { 2 } , - \frac { 19 } { 4 } \right)$ 
D)  $\left( \frac { 1 } { 2 } , - \frac { 15 } { 4 } \right)$

Write the equation of the parabola that has the same shape as the given parabola but with the given vertex. - $f ( x ) = 5 x ^ { 2 } ; ( - 1,3 )$

Use the quadratic formula to solve the equation. - $x ( x - 10 ) = 3$

Solve. -An isosceles right triangle has legs of equal length. If the hypotenuse is 22 inches long, find the length of each leg.

Use the square root property to solve the equation. - $( 5 x + 5 ) ^ { 2 } = 100$

Use the quadratic formula to solve the equation. - $4 x ^ { 2 } + 6 x + 1 = 0$

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

Write the equation of the parabola that has the same shape as the given parabola but with the given vertex. - $f ( x ) = - 4 x ^ { 2 } ; ( 3,7 )$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f(x)=-4(x+2)^{2}-5$ $Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=-4(x+2)^{2}-5$

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

Use the quadratic formula to solve the equation. - $\frac { x ^ { 2 } } { 16 } + x + \frac { 41 } { 16 } = 0$

Use the quadratic formula to solve the equation. - $16 x ^ { 2 } + 1 = 5 x$

Fill in the blank with one of the words or phrases listed below. quadratic formula quadratic discriminant \pm completing the square quadratic inequality (h,k) (0,k) (h,0) -The ---------helps us find the number and type of solutions of a quadratic equation.

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

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $x ^ { 2 } + 6 x - 7 \geq 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - x ^ { 2 } + 6 x - 7 \geq 0$

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - $x ^ { 2 } + \frac { 2 } { 11 } x +$ ____

Use the discriminant to determine the number and type of solutions of the equation. - $x ^ { 2 } - 3 x + 4 = 0$

Use the square root property to solve the equation. - $x ^ { 2 } + 144 = 0$

Solve the equation by completing the square. - $x ^ { 2 } + 5 x - 5 = 0$

Find the vertex of the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } + x - 4$

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

Write the equation of the parabola that has the same shape as the given parabola but with the given vertex. - f(x)=5x2;(−1,3)f ( x ) = 5 x ^ { 2 } ; ( - 1,3 )f(x)=5x2;(−1,3)

Use the quadratic formula to solve the equation. - x(x−10)=3x ( x - 10 ) = 3x(x−10)=3

Solve. -An isosceles right triangle has legs of equal length. If the hypotenuse is 22 inches long, find the length of each leg.

Use the square root property to solve the equation. - (5x+5)2=100( 5 x + 5 ) ^ { 2 } = 100(5x+5)2=100

Use the quadratic formula to solve the equation. - 4x2+6x+1=04 x ^ { 2 } + 6 x + 1 = 04x2+6x+1=0

Use the square root property to solve the equation. - x2=16x ^ { 2 } = 16x2=16

Write the equation of the parabola that has the same shape as the given parabola but with the given vertex. - f(x)=−4x2;(3,7)f ( x ) = - 4 x ^ { 2 } ; ( 3,7 )f(x)=−4x2;(3,7)

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=−4(x+2)2−5f(x)=-4(x+2)^{2}-5f(x)=−4(x+2)2−5

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

Use the quadratic formula to solve the equation. - x216+x+4116=0\frac { x ^ { 2 } } { 16 } + x + \frac { 41 } { 16 } = 016x2​+x+1641​=0

Use the quadratic formula to solve the equation. - 16x2+1=5x16 x ^ { 2 } + 1 = 5 x16x2+1=5x