Question 1

Simplify $\frac { 2 + i } { 5 + 2 i }$ and write the answer in standard form.

Accepted Answer

A)  $- \frac { 12 } { 29 } + \frac { 1 } { 29 } i$ 
B)  $\frac { 12 } { 29 } - \frac { 1 } { 29 } i$ 
C)  $\frac { 12 } { 29 } + \frac { 1 } { 29 } i$ 
D)  $\frac { 1 } { 29 } + \frac { 12 } { 29 } i$ 
E)  $\frac { 1 } { 29 } - \frac { 12 } { 29 } i$ 
A)  $- \frac { 12 } { 29 } + \frac { 1 } { 29 } i$ 
B)  $\frac { 12 } { 29 } - \frac { 1 } { 29 } i$ 
C)  $\frac { 12 } { 29 } + \frac { 1 } { 29 } i$ 
D)  $\frac { 1 } { 29 } + \frac { 12 } { 29 } i$ 
E)  $\frac { 1 } { 29 } - \frac { 12 } { 29 } i$

Question 2

Simplify $\frac { 1 - 2 i } { 5 i }$ and write the answer in standard form.

Accepted Answer

A)  $\frac { 2 } { 5 } - \frac { i } { 5 }$ 
B)  $- \frac { 2 } { 5 } - \frac { i } { 5 }$ 
C)  $- \frac { 2 } { 5 } + \frac { i } { 5 }$ 
D)  $\frac { 1 } { 5 } - \frac { 2 i } { 5 }$ 
E)  $- \frac { 1 } { 5 } - \frac { 2 i } { 5 }$ 
A)  $\frac { 2 } { 5 } - \frac { i } { 5 }$ 
B)  $- \frac { 2 } { 5 } - \frac { i } { 5 }$ 
C)  $- \frac { 2 } { 5 } + \frac { i } { 5 }$ 
D)  $\frac { 1 } { 5 } - \frac { 2 i } { 5 }$ 
E)  $- \frac { 1 } { 5 } - \frac { 2 i } { 5 }$

Question 3

Use long division to divide.
$$\left( 6 x ^ { 2 } - 20 x + 6 \right) \div ( x - 3 )$$

Accepted Answer

A)  $6 x - 38 + \frac { 120 } { x - 3 }$ 
B)  $6 x - 2$ 
C)  $6 x - 38 + \frac { 40 } { x - 3 }$ 
D)  $6 x - 40$ 
E)  $- 6 x + 2$ 
A)  $6 x - 38 + \frac { 120 } { x - 3 }$ 
B)  $6 x - 2$ 
C)  $6 x - 38 + \frac { 40 } { x - 3 }$ 
D)  $6 x - 40$ 
E)  $- 6 x + 2$

Question 4

Suppose the IQ scores $( y$, rounded to the nearest $10 )$ for a group of people are summarized in the table below. Use the regression feature of a graphing utility to find a quadratic function of the form $y = a x ^ { 2 } + b x + c$ for the data.
$\begin{array}{|c|c|}
\hline \text { IQ Score } & \text { Number of People } \
\boldsymbol{y} & \boldsymbol{x} \
\hline 70 & 50 \
\hline 80 & 76 \
\hline 90 & 89 \
\hline 100 & 93 \
\hline 110 & 74 \
\hline 120 & 53 \
\hline 130 & 16 \
\hline
\end{array}$

Accepted Answer

A)  $y = - 0.04 x ^ { 2 } + 15.08 x - 411.58$ 
B)  $y = - 0.06 x ^ { 2 } + 12.06 x - 484.21$ 
C)  $y = - 0.08 x ^ { 2 } + 10.98 x - 508.43$ 
D)  $y = - 0.07 x ^ { 2 } + 13.63 x - 460$ 
E)  $y = - 0.09 x ^ { 2 } + 8.56 x - 556.85$ 
A)  $y = - 0.04 x ^ { 2 } + 15.08 x - 411.58$ 
B)  $y = - 0.06 x ^ { 2 } + 12.06 x - 484.21$ 
C)  $y = - 0.08 x ^ { 2 } + 10.98 x - 508.43$ 
D)  $y = - 0.07 x ^ { 2 } + 13.63 x - 460$ 
E)  $y = - 0.09 x ^ { 2 } + 8.56 x - 556.85$

Question 5

Using the factors $( x + 4 )$ and $( x + 3 )$, find the remaining factor(s) of $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } + 5 x - 12$ and write the polynomial in fully factored form.

Accepted Answer

A)  $f ( x ) = ( x + 4 ) ( x + 3 ) ( x - 1 )$ 
B)  $f ( x ) = ( x + 4 ) ( x + 3 ) ^ { 2 }$ 
C)  $f ( x ) = ( x + 4 ) ( x + 3 ) ( x + 1 )$ 
D)  $f ( x ) = ( x + 4 ) ^ { 2 } ( x + 3 )$ 
E)  $\quad f ( x ) = ( x + 4 ) ( x + 3 ) ( x + 3 )$ 
A)  $f ( x ) = ( x + 4 ) ( x + 3 ) ( x - 1 )$ 
B)  $f ( x ) = ( x + 4 ) ( x + 3 ) ^ { 2 }$ 
C)  $f ( x ) = ( x + 4 ) ( x + 3 ) ( x + 1 )$ 
D)  $f ( x ) = ( x + 4 ) ^ { 2 } ( x + 3 )$ 
E)  $\quad f ( x ) = ( x + 4 ) ( x + 3 ) ( x + 3 )$

Question 6

Determine the value that $f ( x ) = \frac { 3 x - 5 } { x - 6 }$ approaches as x increases and decreases in magnitude without bound.

Accepted Answer

A)  6 
B)  5 
C)  4 
D)  3 
E)  2 
A)  6 
B)  5 
C)  4 
D)  3 
E)  2

Question 7

Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one. $- 4 , - 1,0,1,4$

Accepted Answer

A)  $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } + 27 x ^ { 2 } + 36 x$ 
B)  $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } - 27 x ^ { 2 } + 36 x$ 
C)  $f ( x ) = x ^ { 5 } + 5 x ^ { 4 } - 19 x ^ { 3 } - 16 x ^ { 2 } + 48 x$ 
D)  $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } - 13 x ^ { 3 } - x ^ { 2 } + 12 x$ 
E)  $f ( x ) = x ^ { 5 } - 17 x ^ { 3 } + 16 x$ 
A)  $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } + 27 x ^ { 2 } + 36 x$ 
B)  $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } - 27 x ^ { 2 } + 36 x$ 
C)  $f ( x ) = x ^ { 5 } + 5 x ^ { 4 } - 19 x ^ { 3 } - 16 x ^ { 2 } + 48 x$ 
D)  $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } - 13 x ^ { 3 } - x ^ { 2 } + 12 x$ 
E)  $f ( x ) = x ^ { 5 } - 17 x ^ { 3 } + 16 x$

Question 8

Simplify $( 3 - 6 i ) ^ { 2 } - ( 3 + 6 i ) ^ { 2 }$ and write the answer in standard form.

Accepted Answer

A)  0 
B)  $- 72 i$ 
C)  $18 - 72 i$ 
D)  $18 + 72 i$ 
E)  $6 - 24 i$ 
A)  0 
B)  $- 72 i$ 
C)  $18 - 72 i$ 
D)  $18 + 72 i$ 
E)  $6 - 24 i$

Question 9

Write the standard form of the equation of the parabola that has a vertex at $\left( \frac { - 2 } { 3 } , \frac { 1 } { 9 } \right)$ and passes through the point $( 3 , - 4 )$.

Accepted Answer

A)  $f ( x ) = - \frac { 37 } { 11 } \left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 1 } { 9 }$ 
B)  $f ( x ) = - \frac { 37 } { 121 } \left( x - \frac { 3 } { 2 } \right) ^ { 2 } + \frac { 1 } { 9 }$ 
C)  $f ( x ) = - \frac { 37 } { 121 } \left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 1 } { 9 }$ 
D)  $f ( x ) = - \frac { 37 } { 11 } \left( x - \frac { 2 } { 3 } \right) ^ { 2 } - \frac { 1 } { 9 }$ 
E)  $f ( x ) = - \frac { 37 } { 25 } \left( x - \frac { 3 } { 2 } \right) ^ { 2 } - \frac { 1 } { 9 }$ 
A)  $f ( x ) = - \frac { 37 } { 11 } \left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 1 } { 9 }$ 
B)  $f ( x ) = - \frac { 37 } { 121 } \left( x - \frac { 3 } { 2 } \right) ^ { 2 } + \frac { 1 } { 9 }$ 
C)  $f ( x ) = - \frac { 37 } { 121 } \left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 1 } { 9 }$ 
D)  $f ( x ) = - \frac { 37 } { 11 } \left( x - \frac { 2 } { 3 } \right) ^ { 2 } - \frac { 1 } { 9 }$ 
E)  $f ( x ) = - \frac { 37 } { 25 } \left( x - \frac { 3 } { 2 } \right) ^ { 2 } - \frac { 1 } { 9 }$

Question 10

Find the quadratic function f whose graph intersects the x-axis at (1,0) and (4,0) and the y-axis at (0,4).

Accepted Answer

A)  $f ( x ) = - x ^ { 2 } - 3 x - 4$ 
B)  $f ( x ) = x ^ { 2 } - 5 x + 4$ 
C)  $f ( x ) = x ^ { 2 } + 3 x + 4$ 
D)  $f ( x ) = - x ^ { 2 } + 3 x + 4$ 
E)  $f ( x ) = - x ^ { 2 } + 5 x + 4$ 
A)  $f ( x ) = - x ^ { 2 } - 3 x - 4$ 
B)  $f ( x ) = x ^ { 2 } - 5 x + 4$ 
C)  $f ( x ) = x ^ { 2 } + 3 x + 4$ 
D)  $f ( x ) = - x ^ { 2 } + 3 x + 4$ 
E)  $f ( x ) = - x ^ { 2 } + 5 x + 4$

Question 11

Sketch the graph of the rational function below.
$f ( x ) = - \frac { x ^ { 2 } - 1 } { x }$

Accepted Answer

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

Question 12

Determine the zeros (if any) of the rational function $g ( x ) = 7 + \frac { 2 } { x ^ { 2 } + 7 }$.

Accepted Answer

A)  $x = - \sqrt { 7 } , x = \sqrt { 7 }$ 
B)  $x = - 2$ 
C)  $x = - \frac { 2 } { 7 } , x = \frac { 2 } { 7 }$ 
D)  $x = - 7 , x = 7$ 
E)  no zeros 
A)  $x = - \sqrt { 7 } , x = \sqrt { 7 }$ 
B)  $x = - 2$ 
C)  $x = - \frac { 2 } { 7 } , x = \frac { 2 } { 7 }$ 
D)  $x = - 7 , x = 7$ 
E)  no zeros

Question 13

Use the regression feature of a graphing utility to find a quadratic model for the data below.
$\begin{array}{|r|c|}
\hline x & y \
\hline-2 & 15.7 \
\hline-1 & 3.5 \
\hline 0 & -2.7 \
\hline 1 & -2.9 \
\hline 2 & 3.7 \
\hline 3 & 15.8 \
\hline 4 & 33.6 \
\hline
\end{array}$

Accepted Answer

A)  $y = 2.89 x ^ { 2 } - 3.35 x - 2.9$ 
B)  $y = 2.73 x ^ { 2 } - 3.2 x - 2.75$ 
C)  $y = 3.34 x ^ { 2 } - 2.9 x - 2.7$ 
D)  $y = 3.19 x ^ { 2 } - 2.74 x - 2.4$ 
E)  $y = 3.04 x ^ { 2 } - 3.05 x - 2.61$ 
A)  $y = 2.89 x ^ { 2 } - 3.35 x - 2.9$ 
B)  $y = 2.73 x ^ { 2 } - 3.2 x - 2.75$ 
C)  $y = 3.34 x ^ { 2 } - 2.9 x - 2.7$ 
D)  $y = 3.19 x ^ { 2 } - 2.74 x - 2.4$ 
E)  $y = 3.04 x ^ { 2 } - 3.05 x - 2.61$

Question 14

Find the zeros of the function below algebraically, if any exist.
$f ( x ) = x ^ { 6 } + 28 x ^ { 3 } + 27$

Accepted Answer

A)  $- 3$ and $- 1$ 
B)  $- 2$ and $- 1$ 
C)  $- 3$ and $- 2$ 
D)  $- 2 , - 1,1$, and 2 
E)  $- 3 , - 2,2$, and 3 
A)  $- 3$ and $- 1$ 
B)  $- 2$ and $- 1$ 
C)  $- 3$ and $- 2$ 
D)  $- 2 , - 1,1$, and 2 
E)  $- 3 , - 2,2$, and 3

Question 15

Determine the domain of the function $f ( x ) = \frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 16 }$.

Accepted Answer

A)  Domain: all real numbers except $x = - 4$ and 3 
B)  Domain: all real numbers except $x = - 16$ 
C)  Domain: all real numbers except $x = - 4$ and $- 3$ 
D)  Domain: all real numbers except $x = 4$ and 3 
E)  Domain: all real numbers 
A)  Domain: all real numbers except $x = - 4$ and 3 
B)  Domain: all real numbers except $x = - 16$ 
C)  Domain: all real numbers except $x = - 4$ and $- 3$ 
D)  Domain: all real numbers except $x = 4$ and 3 
E)  Domain: all real numbers

Question 16

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

Accepted Answer

A)  $( 0 , - 2 )$ 
B)  $( 2,0 )$ 
C)  $( 2,2 )$ 
D)  $( 0,2 )$ 
E)  $( - 2,0 )$ 
A)  $( 0 , - 2 )$ 
B)  $( 2,0 )$ 
C)  $( 2,2 )$ 
D)  $( 0,2 )$ 
E)  $( - 2,0 )$

Question 17

Write the standard form of the equation of the parabola that has a vertex at $( 3,8 )$ and passes through the point $( 5 , - 2 )$.

Accepted Answer

A)  $f ( x ) = - \frac { 1 } { 2 } ( x - 3 ) ^ { 2 } + 5$ 
B)  $f ( x ) = - \frac { 5 } { 2 } ( x - 3 ) ^ { 2 } + 8$ 
C)  $f ( x ) = - \frac { 10 } { 9 } ( x + 3 ) ^ { 2 } + 8$ 
D)  $f ( x ) = \frac { 8 } { 5 } ( x - 8 ) ^ { 2 } - 2$ 
E)  $f ( x ) = \frac { 8 } { 9 } ( x - 8 ) ^ { 2 } - 5$ 
A)  $f ( x ) = - \frac { 1 } { 2 } ( x - 3 ) ^ { 2 } + 5$ 
B)  $f ( x ) = - \frac { 5 } { 2 } ( x - 3 ) ^ { 2 } + 8$ 
C)  $f ( x ) = - \frac { 10 } { 9 } ( x + 3 ) ^ { 2 } + 8$ 
D)  $f ( x ) = \frac { 8 } { 5 } ( x - 8 ) ^ { 2 } - 2$ 
E)  $f ( x ) = \frac { 8 } { 9 } ( x - 8 ) ^ { 2 } - 5$

Question 18

Simplify $( \sqrt { - 2 } ) ^ { 11 }$ and write the answer in standard form.

Accepted Answer

A)  $32 \sqrt { 2 } i$ 
B)  $- 32 \sqrt { 2 } i$ 
C)  $1024 \sqrt { 2 } i$ 
D)  $- 32 \sqrt { 2 }$ 
E)  The expression cannot be simplified. 
A)  $32 \sqrt { 2 } i$ 
B)  $- 32 \sqrt { 2 } i$ 
C)  $1024 \sqrt { 2 } i$ 
D)  $- 32 \sqrt { 2 }$ 
E)  The expression cannot be simplified.

Question 19

Use the regression feature of a graphing utility to find a quadratic model for the data below. $\begin{array}{|r|c|}
\hline \boldsymbol{x} & \boldsymbol{y} \
\hline-2 & 9.8 \
\hline-1 & 4.1 \
\hline 0 & 3.3 \
\hline 1 & 6.6 \
\hline 2 & 13.8 \
\hline 3 & 24.1 \
\hline 4 & 39.5 \
\hline
\end{array}$

Accepted Answer

A)  $y = 1.91 x ^ { 2 } + 1.06 x + 3.15$ 
B)  $y = 1.81 x ^ { 2 } + 1.02 x + 3.3$ 
C)  $y = 2.21 x ^ { 2 } + 0.92 x + 3.3$ 
D)  $y = 2.11 x ^ { 2 } + 0.87 x + 3.65$ 
E)  $y = 2.01 x ^ { 2 } + 0.97 x + 3.44$ 
A)  $y = 1.91 x ^ { 2 } + 1.06 x + 3.15$ 
B)  $y = 1.81 x ^ { 2 } + 1.02 x + 3.3$ 
C)  $y = 2.21 x ^ { 2 } + 0.92 x + 3.3$ 
D)  $y = 2.11 x ^ { 2 } + 0.87 x + 3.65$ 
E)  $y = 2.01 x ^ { 2 } + 0.97 x + 3.44$

Question 20

Determine the $x$-intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } + 6 x + 10$.

Accepted Answer

A)  $( - 8,0 ) , ( 1,0 )$ 
B)  $( - 3,0 ) , ( 7,0 )$ 
C)  $( - 1,0 ) , ( - 6,0 )$ 
D)  $( - 8,0 ) , ( - 6,0 )$ 
E)  no $x$-intercept(s) 
A)  $( - 8,0 ) , ( 1,0 )$ 
B)  $( - 3,0 ) , ( 7,0 )$ 
C)  $( - 1,0 ) , ( - 6,0 )$ 
D)  $( - 8,0 ) , ( - 6,0 )$ 
E)  no $x$-intercept(s)

Simplify $\frac { 2 + i } { 5 + 2 i }$ and write the answer in standard form.

Simplify $\frac { 1 - 2 i } { 5 i }$ and write the answer in standard form.

Use long division to divide. $\left( 6 x ^ { 2 } - 20 x + 6 \right) \div ( x - 3 )$

Using the factors $( x + 4 )$ and $( x + 3 )$ , find the remaining factor(s) of $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } + 5 x - 12$ and write the polynomial in fully factored form.

Determine the value that $f ( x ) = \frac { 3 x - 5 } { x - 6 }$ approaches as x increases and decreases in magnitude without bound.

Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one. $- 4 , - 1,0,1,4$

Simplify $( 3 - 6 i ) ^ { 2 } - ( 3 + 6 i ) ^ { 2 }$ and write the answer in standard form.

Write the standard form of the equation of the parabola that has a vertex at $\left( \frac { - 2 } { 3 } , \frac { 1 } { 9 } \right)$ and passes through the point $( 3 , - 4 )$ .

Find the quadratic function f whose graph intersects the x-axis at (1,0) and (4,0) and the y-axis at (0,4).

Sketch the graph of the rational function below. $f ( x ) = - \frac { x ^ { 2 } - 1 } { x }$

Determine the zeros (if any) of the rational function $g ( x ) = 7 + \frac { 2 } { x ^ { 2 } + 7 }$ .

Use the regression feature of a graphing utility to find a quadratic model for the data below. x y -2 15.7 -1 3.5 0 -2.7 1 -2.9 2 3.7 3 15.8 4 33.6

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 6 } + 28 x ^ { 3 } + 27$

Determine the domain of the function $f ( x ) = \frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 16 }$ .

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

Write the standard form of the equation of the parabola that has a vertex at $( 3,8 )$ and passes through the point $( 5 , - 2 )$ .

Simplify $( \sqrt { - 2 } ) ^ { 11 }$ and write the answer in standard form.

Use the regression feature of a graphing utility to find a quadratic model for the data below. -2 9.8 -1 4.1 0 3.3 1 6.6 2 13.8 3 24.1 4 39.5

Determine the $x$ -intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } + 6 x + 10$ .

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Exam 2: Polynomial and Rational Functions

Simplify 2+i5+2i\frac { 2 + i } { 5 + 2 i }5+2i2+i​ and write the answer in standard form.

Simplify 1−2i5i\frac { 1 - 2 i } { 5 i }5i1−2i​ and write the answer in standard form.

Use long division to divide. (6x2−20x+6)÷(x−3)\left( 6 x ^ { 2 } - 20 x + 6 \right) \div ( x - 3 )(6x2−20x+6)÷(x−3)

Using the factors (x+4)( x + 4 )(x+4) and (x+3)( x + 3 )(x+3) , find the remaining factor(s) of f(x)=x3+6x2+5x−12f ( x ) = x ^ { 3 } + 6 x ^ { 2 } + 5 x - 12f(x)=x3+6x2+5x−12 and write the polynomial in fully factored form.

Determine the value that f(x)=3x−5x−6f ( x ) = \frac { 3 x - 5 } { x - 6 }f(x)=x−63x−5​ approaches as x increases and decreases in magnitude without bound.

Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one. −4,−1,0,1,4- 4 , - 1,0,1,4−4,−1,0,1,4

Simplify (3−6i)2−(3+6i)2( 3 - 6 i ) ^ { 2 } - ( 3 + 6 i ) ^ { 2 }(3−6i)2−(3+6i)2 and write the answer in standard form.

Write the standard form of the equation of the parabola that has a vertex at (−23,19)\left( \frac { - 2 } { 3 } , \frac { 1 } { 9 } \right)(3−2​,91​) and passes through the point (3,−4)( 3 , - 4 )(3,−4) .

Find the quadratic function f whose graph intersects the x-axis at (1,0) and (4,0) and the y-axis at (0,4).

Sketch the graph of the rational function below. f(x)=−x2−1xf ( x ) = - \frac { x ^ { 2 } - 1 } { x }f(x)=−xx2−1​

Determine the zeros (if any) of the rational function g(x)=7+2x2+7g ( x ) = 7 + \frac { 2 } { x ^ { 2 } + 7 }g(x)=7+x2+72​ .

Use the regression feature of a graphing utility to find a quadratic model for the data below. x y -2 15.7 -1 3.5 0 -2.7 1 -2.9 2 3.7 3 15.8 4 33.6

Find the zeros of the function below algebraically, if any exist. f(x)=x6+28x3+27f ( x ) = x ^ { 6 } + 28 x ^ { 3 } + 27f(x)=x6+28x3+27

Determine the domain of the function f(x)=x2+7x+12x2+16f ( x ) = \frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 16 }f(x)=x2+16x2+7x+12​ .

Determine the vertex of the graph of the quadratic function f(x)=x2+2f ( x ) = x ^ { 2 } + 2f(x)=x2+2 .

Write the standard form of the equation of the parabola that has a vertex at (3,8)( 3,8 )(3,8) and passes through the point (5,−2)( 5 , - 2 )(5,−2) .

Simplify (−2)11( \sqrt { - 2 } ) ^ { 11 }(−2​)11 and write the answer in standard form.

Use the regression feature of a graphing utility to find a quadratic model for the data below. -2 9.8 -1 4.1 0 3.3 1 6.6 2 13.8 3 24.1 4 39.5

Determine the xxx -intercept(s) of the quadratic function f(x)=x2+6x+10f ( x ) = x ^ { 2 } + 6 x + 10f(x)=x2+6x+10 .

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Simplify $\frac { 2 + i } { 5 + 2 i }$ and write the answer in standard form.

Simplify $\frac { 1 - 2 i } { 5 i }$ and write the answer in standard form.

Use long division to divide. $\left( 6 x ^ { 2 } - 20 x + 6 \right) \div ( x - 3 )$

Using the factors $( x + 4 )$ and $( x + 3 )$ , find the remaining factor(s) of $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } + 5 x - 12$ and write the polynomial in fully factored form.

Determine the value that $f ( x ) = \frac { 3 x - 5 } { x - 6 }$ approaches as x increases and decreases in magnitude without bound.

Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one. $- 4 , - 1,0,1,4$

Simplify $( 3 - 6 i ) ^ { 2 } - ( 3 + 6 i ) ^ { 2 }$ and write the answer in standard form.

Write the standard form of the equation of the parabola that has a vertex at $\left( \frac { - 2 } { 3 } , \frac { 1 } { 9 } \right)$ and passes through the point $( 3 , - 4 )$ .

Sketch the graph of the rational function below. $f ( x ) = - \frac { x ^ { 2 } - 1 } { x }$

Determine the zeros (if any) of the rational function $g ( x ) = 7 + \frac { 2 } { x ^ { 2 } + 7 }$ .

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 6 } + 28 x ^ { 3 } + 27$

Determine the domain of the function $f ( x ) = \frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 16 }$ .

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

Write the standard form of the equation of the parabola that has a vertex at $( 3,8 )$ and passes through the point $( 5 , - 2 )$ .

Simplify $( \sqrt { - 2 } ) ^ { 11 }$ and write the answer in standard form.

Determine the $x$ -intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } + 6 x + 10$ .