Question 1

Use the quadratic formula to solve the equation.
-$x ^ { 2 } + 30 x + 225 = 0$

Accepted Answer

A)  $- 15,15$ 
B)  $15 - i , 15 + i$ 
C)  15 
D)  $- 15$ 
A)  $- 15,15$ 
B)  $15 - i , 15 + i$ 
C)  15 
D)  $- 15$

Question 2

Use the quadratic formula to solve the equation.
-$x ^ { 2 } + 10 x + 3 = 0$

Accepted Answer

A)  $5 - \sqrt { 3 } , 5 + \sqrt { 3 }$ 
B)  $- 10 + \sqrt { 3 }$ 
C)  $- 5 - \sqrt { 22 } , - 5 + \sqrt { 22 }$ 
D)  $5 + \sqrt { 22 }$ 
A)  $5 - \sqrt { 3 } , 5 + \sqrt { 3 }$ 
B)  $- 10 + \sqrt { 3 }$ 
C)  $- 5 - \sqrt { 22 } , - 5 + \sqrt { 22 }$ 
D)  $5 + \sqrt { 22 }$

Question 3

Find the vertex of the graph of the quadratic function.
-$f ( x ) = x ^ { 2 } - 11 x - 7$

Accepted Answer

A)  $( 13 , - 7 )$ 
B)  $( - 11,235 )$ 
C)  $\left[ - \frac { 11 } { 2 } , \frac { 335 } { 4 } \right]$ 
D)  $\left( \frac { 11 } { 2 } , - \frac { 149 } { 4 } \right)$ 
A)  $( 13 , - 7 )$ 
B)  $( - 11,235 )$ 
C)  $\left[ - \frac { 11 } { 2 } , \frac { 335 } { 4 } \right]$ 
D)  $\left( \frac { 11 } { 2 } , - \frac { 149 } { 4 } \right)$

Question 4

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

Accepted Answer

A)  vertex $( 0,0 )$; axis $x = 0$
  
B)  vertex $( 0 , - 2 )$; axis $x = 0$
  
C)  vertex $( 0,0 )$; axis $x = 0$
  
D)  vertex $( 0,0 )$; axis $x = 0$
  
A)  vertex $( 0,0 )$; axis $x = 0$
  
B)  vertex $( 0 , - 2 )$; axis $x = 0$
  
C)  vertex $( 0,0 )$; axis $x = 0$
  
D)  vertex $( 0,0 )$; axis $x = 0$

Question 5

Find the vertex of the graph of the quadratic function.
-$f ( x ) = x ^ { 2 } + 6 x - 7$

Accepted Answer

A)  $( 6,65 )$ 
B)  $( - 3 , - 34 )$ 
C)  $( 3,20 )$ 
D)  $( - 3 , - 16 )$ 
A)  $( 6,65 )$ 
B)  $( - 3 , - 34 )$ 
C)  $( 3,20 )$ 
D)  $( - 3 , - 16 )$

Question 6

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l l } 
\text { quadratic formula } & \text { quadratic } & \text { discriminant } & \pm \sqrt { b } \
\text { completing the square } & \text { quadratic inequality } & ( h , k ) & ( 0 , k ) \
( h , 0 ) & \frac { - b } { 2 a } & &
\end{array}$$
-A ______equation is one that can be written in the form $a x ^ { 2 } + b x + c = 0$ where $a , b$, and $c$ are real numbers and a is not 0 .

Accepted Answer

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

Question 7

Use the square root property to solve the equation.
-$5 x ^ { 2 } = 75$

Accepted Answer

A)  $- \sqrt { 15 } , \sqrt { 15 }$ 
B)  $- 15,15$ 
C)  $37.5$ 
D)  16 
A)  $- \sqrt { 15 } , \sqrt { 15 }$ 
B)  $- 15,15$ 
C)  $37.5$ 
D)  16

Question 8

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

Question 9

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 10

Solve.
-An arrow is fired into the air with an initial velocity of 96 feet per second. The height in feet of the arrow $t$ seconds after it was shot into the air is given by the function $h ( t ) = - 16 t ^ { 2 } + 96 t$. Find the maximum height of the arrow.

Accepted Answer

A)  $432 \mathrm { ft }$ 
B)  $144 \mathrm { ft }$ 
C)  $48 \mathrm { ft }$ 
D)  $240 \mathrm { ft }$ 
A)  $432 \mathrm { ft }$ 
B)  $144 \mathrm { ft }$ 
C)  $48 \mathrm { ft }$ 
D)  $240 \mathrm { ft }$

Question 11

Use the square root property to solve the equation.
-$( 2 x - 3 ) ^ { 2 } = 25$

Accepted Answer

A)  $8 , - 2$ 
B)  $2 , - 8$ 
C)  $1 , - 4$ 
D)  $4 , - 1$ 
A)  $8 , - 2$ 
B)  $2 , - 8$ 
C)  $1 , - 4$ 
D)  $4 , - 1$

Question 12

Solve the equation by completing the square.
-$x ^ { 2 } + x + 9 = 0$

Accepted Answer

A)  $\frac { 1 - \sqrt { 35 } } { 2 } , \frac { 1 + \sqrt { 35 } } { 2 }$ 
B)  $\frac { 1 - \mathrm { i } \sqrt { 35 } } { 2 } , \frac { 1 + \mathrm { i } \sqrt { 35 } } { 2 }$ 
C)  $\frac { - 1 - \sqrt { 35 } } { 2 } , \frac { - 1 + \sqrt { 35 } } { 2 }$ 
D)  $\frac { - 1 - i \sqrt { 35 } } { 2 } , \frac { - 1 + i \sqrt { 35 } } { 2 }$ 
A)  $\frac { 1 - \sqrt { 35 } } { 2 } , \frac { 1 + \sqrt { 35 } } { 2 }$ 
B)  $\frac { 1 - \mathrm { i } \sqrt { 35 } } { 2 } , \frac { 1 + \mathrm { i } \sqrt { 35 } } { 2 }$ 
C)  $\frac { - 1 - \sqrt { 35 } } { 2 } , \frac { - 1 + \sqrt { 35 } } { 2 }$ 
D)  $\frac { - 1 - i \sqrt { 35 } } { 2 } , \frac { - 1 + i \sqrt { 35 } } { 2 }$

Question 13

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

Accepted Answer

A)  $( - \infty , - 3 ) \cup ( 7 , \infty )$
  
B)  $( 7 , \infty )$
  
C)  $( - 3,7 )$
  
D)  $( - \infty , - 3 )$
  
A)  $( - \infty , - 3 ) \cup ( 7 , \infty )$
  
B)  $( 7 , \infty )$
  
C)  $( - 3,7 )$
  
D)  $( - \infty , - 3 )$

Question 14

Use the discriminant to determine the number and type of solutions of the equation.
-$4 x ^ { 2 } = 6 x - 8$

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 15

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$16 \mathrm { x } ^ { 3 } + 48 \mathrm { x } ^ { 2 } - 25 \mathrm { x } - 75 > 0$

Accepted Answer

A)  $( - \infty , - 3 ] \cup \left[ - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$
  
B)  $( - \infty , - 3 ) \cup \left( - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right)$
  
C)  $\left( - 3 , - \frac { 5 } { 4 } \right) \cup \left( \frac { 5 } { 4 } , \infty \right)$
  
D)  $\left[ - 3 , - \frac { 5 } { 4 } \right] \cup \left[ \frac { 5 } { 4 } , \infty \right)$
  
A)  $( - \infty , - 3 ] \cup \left[ - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$
  
B)  $( - \infty , - 3 ) \cup \left( - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right)$
  
C)  $\left( - 3 , - \frac { 5 } { 4 } \right) \cup \left( \frac { 5 } { 4 } , \infty \right)$
  
D)  $\left[ - 3 , - \frac { 5 } { 4 } \right] \cup \left[ \frac { 5 } { 4 } , \infty \right)$

Question 16

Find two possible missing terms so that the expression is a perfect square trinomial.
-x2+---------+10

Accepted Answer

A)  $\ { - 20 } 0 x , 200 x$ 
B)  $- 50 x , 50 x$ 
C)  $- 10 x , 10 x$ 
D)  $- 20 \mathrm { x } , 20 \mathrm { x }$ 
A)  $\ { - 20 } 0 x , 200 x$ 
B)  $- 50 x , 50 x$ 
C)  $- 10 x , 10 x$ 
D)  $- 20 \mathrm { x } , 20 \mathrm { x }$

Question 17

Solve.
-$x ^ { 4 } - 30 x ^ { 2 } = 216$

Accepted Answer

A)  $- 6,6 , - i \sqrt { 6 } , i \sqrt { 6 }$ 
B)  $- \sqrt { 6 } , \sqrt { 6 } , - 6 i , 6 i$, 
C)  $6 , \mathrm { i } \sqrt { 6 }$ 
D)  $- 36,6$ 
A)  $- 6,6 , - i \sqrt { 6 } , i \sqrt { 6 }$ 
B)  $- \sqrt { 6 } , \sqrt { 6 } , - 6 i , 6 i$, 
C)  $6 , \mathrm { i } \sqrt { 6 }$ 
D)  $- 36,6$

Question 18

Solve.
-$\frac { 7 } { x ^ { 2 } - 15 x + 54 } = \frac { 2 x } { x - 9 } - \frac { x } { x - 6 }$

Accepted Answer

A)  $\frac { - 3 - i \sqrt { 19 } } { 2 } , \frac { - 3 + i \sqrt { 19 } } { 2 }$ 
B)  $\frac { 3 - \sqrt { 37 } } { 2 } , \frac { 3 + \sqrt { 37 } } { 2 }$ 
C)  $\frac { - 3 - \sqrt { 37 } } { 2 } , \frac { - 3 + \sqrt { 37 } } { 2 }$ 
D)  $\frac { 3 - i \sqrt { 19 } } { 2 } , \frac { 3 + i \sqrt { 19 } } { 2 }$ 
A)  $\frac { - 3 - i \sqrt { 19 } } { 2 } , \frac { - 3 + i \sqrt { 19 } } { 2 }$ 
B)  $\frac { 3 - \sqrt { 37 } } { 2 } , \frac { 3 + \sqrt { 37 } } { 2 }$ 
C)  $\frac { - 3 - \sqrt { 37 } } { 2 } , \frac { - 3 + \sqrt { 37 } } { 2 }$ 
D)  $\frac { 3 - i \sqrt { 19 } } { 2 } , \frac { 3 + i \sqrt { 19 } } { 2 }$

Question 19

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 graph of $x ^ { 2 } + k$ has vertex_______

Accepted Answer

A)  $( h , k )$ 
B)  $( h , 0 )$ 
C)  $\pm \sqrt { b }$ 
D)  $( 0 , k )$ 
A)  $( h , k )$ 
B)  $( h , 0 )$ 
C)  $\pm \sqrt { b }$ 
D)  $( 0 , k )$

Question 20

Use the discriminant to determine the number and type of solutions of the equation.
-$1 + 5 x ^ { 2 } = 2 x$

Accepted Answer

A)  one real solution 
B)  two real solutions 
C)  two complex but not real solutions 
A)  one real solution 
B)  two real solutions 
C)  two complex but not real solutions

Use the quadratic formula to solve the equation. - $x ^ { 2 } + 30 x + 225 = 0$

Use the quadratic formula to solve the equation. - $x ^ { 2 } + 10 x + 3 = 0$

Find the vertex of the graph of the quadratic function. - $f ( x ) = x ^ { 2 } - 11 x - 7$

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

Find the vertex of the graph of the quadratic function. - $f ( x ) = x ^ { 2 } + 6 x - 7$

Use the square root property to solve the equation. - $5 x ^ { 2 } = 75$

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

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

Solve. -An arrow is fired into the air with an initial velocity of 96 feet per second. The height in feet of the arrow $t$ seconds after it was shot into the air is given by the function $h ( t ) = - 16 t ^ { 2 } + 96 t$ . Find the maximum height of the arrow.

Use the square root property to solve the equation. - $( 2 x - 3 ) ^ { 2 } = 25$

Solve the equation by completing the square. - $x ^ { 2 } + x + 9 = 0$

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

Use the discriminant to determine the number and type of solutions of the equation. - $4 x ^ { 2 } = 6 x - 8$

Find two possible missing terms so that the expression is a perfect square trinomial. -x²+---------+10

Solve. - $x ^ { 4 } - 30 x ^ { 2 } = 216$

Solve. - $\frac { 7 } { x ^ { 2 } - 15 x + 54 } = \frac { 2 x } { x - 9 } - \frac { x } { x - 6 }$

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 graph of $x ^ { 2 } + k$ has vertex_______

Use the discriminant to determine the number and type of solutions of the equation. - $1 + 5 x ^ { 2 } = 2 x$

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. - x2+30x+225=0x ^ { 2 } + 30 x + 225 = 0x2+30x+225=0

Use the quadratic formula to solve the equation. - x2+10x+3=0x ^ { 2 } + 10 x + 3 = 0x2+10x+3=0

Find the vertex of the graph of the quadratic function. - f(x)=x2−11x−7f ( x ) = x ^ { 2 } - 11 x - 7f(x)=x2−11x−7

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=−2x2f(x)=-2 x^{2}f(x)=−2x2

Find the vertex of the graph of the quadratic function. - f(x)=x2+6x−7f ( x ) = x ^ { 2 } + 6 x - 7f(x)=x2+6x−7

Use the square root property to solve the equation. - 5x2=755 x ^ { 2 } = 755x2=75

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - x2−211x+x ^ { 2 } - \frac { 2 } { 11 } x +x2−112​x+ ____

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. -An arrow is fired into the air with an initial velocity of 96 feet per second. The height in feet of the arrow ttt seconds after it was shot into the air is given by the function h(t)=−16t2+96th ( t ) = - 16 t ^ { 2 } + 96 th(t)=−16t2+96t . Find the maximum height of the arrow.

Use the square root property to solve the equation. - (2x−3)2=25( 2 x - 3 ) ^ { 2 } = 25(2x−3)2=25

Solve the equation by completing the square. - x2+x+9=0x ^ { 2 } + x + 9 = 0x2+x+9=0

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

Use the discriminant to determine the number and type of solutions of the equation. - 4x2=6x−84 x ^ { 2 } = 6 x - 84x2=6x−8

Solve the inequality. Graph the solution set and write the solution set in interval notation. - 16x3+48x2−25x−75>016 \mathrm { x } ^ { 3 } + 48 \mathrm { x } ^ { 2 } - 25 \mathrm { x } - 75 > 016x3+48x2−25x−75>0

Find two possible missing terms so that the expression is a perfect square trinomial. -x2+---------+10

Solve. - x4−30x2=216x ^ { 4 } - 30 x ^ { 2 } = 216x4−30x2=216

Solve. - 7x2−15x+54=2xx−9−xx−6\frac { 7 } { x ^ { 2 } - 15 x + 54 } = \frac { 2 x } { x - 9 } - \frac { x } { x - 6 }x2−15x+547​=x−92x​−x−6x​

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 graph of x2+kx ^ { 2 } + kx2+k has vertex_______

Use the discriminant to determine the number and type of solutions of the equation. - 1+5x2=2x1 + 5 x ^ { 2 } = 2 x1+5x2=2x