Question 1

A polynomial function $f$ has degree 3 , the zeros below, and a solution point of $f ( - 3 ) = - 4$. Write $f$ in completely factored form.
$- 4 , - 3 + 2 i$

Accepted Answer

A)  $f ( x ) = ( x + 3 ) ( x + 4 - 2 i ) ( x + 4 + 2 i )$ 
B)  $f ( x ) = - ( x + 4 ) ( x + 2 - 3 i ) ( x + 2 + 3 i )$ 
C)  $f ( x ) = ( x + 4 ) ( x + 2 - 3 i ) ( x + 2 + 3 i )$ 
D)  $f ( x ) = - ( x + 4 ) ( x + 3 - 2 i ) ( x + 3 + 2 i )$ 
E)  $\quad f ( x ) = ( x + 4 ) ( x + 3 - 2 i ) ( x + 3 + 2 i )$ 
A)  $f ( x ) = ( x + 3 ) ( x + 4 - 2 i ) ( x + 4 + 2 i )$ 
B)  $f ( x ) = - ( x + 4 ) ( x + 2 - 3 i ) ( x + 2 + 3 i )$ 
C)  $f ( x ) = ( x + 4 ) ( x + 2 - 3 i ) ( x + 2 + 3 i )$ 
D)  $f ( x ) = - ( x + 4 ) ( x + 3 - 2 i ) ( x + 3 + 2 i )$ 
E)  $\quad f ( x ) = ( x + 4 ) ( x + 3 - 2 i ) ( x + 3 + 2 i )$

Question 2

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 3

Determine the $x$-intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } - 15 x + 56$.

Accepted Answer

A)  $( 8,0 ) , ( 7,0 )$ 
B)  $( - 4,0 ) , ( - 8,0 )$ 
C)  $( - 8,0 ) , ( - 7,0 )$ 
D)  $( 4,0 ) , ( 8,0 )$ 
E)  no $x$-intercept(s) 
A)  $( 8,0 ) , ( 7,0 )$ 
B)  $( - 4,0 ) , ( - 8,0 )$ 
C)  $( - 8,0 ) , ( - 7,0 )$ 
D)  $( 4,0 ) , ( 8,0 )$ 
E)  no $x$-intercept(s)

Question 4

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 5

Find real numbers $a$ and $b$ such that the equation $a + b i = - 10 + 10 i$ is true.

Accepted Answer

A)  $a = 10 , b = - 10$ 
B)  $\quad a = - 10 , b = - 10$ 
C)  $\quad a = 10 , b = 10$ 
D)  $a = - 10 , b = 10$ 
E)  $\quad a = - 20 , b = 0$ 
A)  $a = 10 , b = - 10$ 
B)  $\quad a = - 10 , b = - 10$ 
C)  $\quad a = 10 , b = 10$ 
D)  $a = - 10 , b = 10$ 
E)  $\quad a = - 20 , b = 0$

Question 6

If $x = \frac { 2 } { 5 }$ is a root of $25 x ^ { 3 } - 70 x ^ { 2 } + 44 x - 8 = 0$, use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Accepted Answer

A)  $( 5 x - 2 ) ( 5 x + 2 ) ( x - 2 ) ; x = \frac { 2 } { 5 } , - \frac { 2 } { 5 } , 2$ 
B)  $( 5 x + 2 ) ^ { 2 } ( x - 2 ) ; x = - \frac { 2 } { 5 } , 2$ 
C)  $( 5 x - 2 ) ( x - 2 ) ^ { 2 } ; x = \frac { 2 } { 5 } , 2$ 
D)  $( 5 x + 2 ) ( x - 2 ) ^ { 2 } ; x = - \frac { 2 } { 5 } , 2$ 
E)  $( 5 x - 2 ) ^ { 2 } ( x - 2 ) ; x = \frac { 2 } { 5 } , 2$ 
A)  $( 5 x - 2 ) ( 5 x + 2 ) ( x - 2 ) ; x = \frac { 2 } { 5 } , - \frac { 2 } { 5 } , 2$ 
B)  $( 5 x + 2 ) ^ { 2 } ( x - 2 ) ; x = - \frac { 2 } { 5 } , 2$ 
C)  $( 5 x - 2 ) ( x - 2 ) ^ { 2 } ; x = \frac { 2 } { 5 } , 2$ 
D)  $( 5 x + 2 ) ( x - 2 ) ^ { 2 } ; x = - \frac { 2 } { 5 } , 2$ 
E)  $( 5 x - 2 ) ^ { 2 } ( x - 2 ) ; x = \frac { 2 } { 5 } , 2$

Question 7

Find all zeros of the function $f ( x ) = x ^ { 2 } ( x - 2 ) \left( x ^ { 3 } - 216 \right)$.

Accepted Answer

A)  $x = 2,216$ 
B)  $x = 0 , - 2 , - 6$ 
C)  $\quad x = 0,2,6 , - 3 - 3 \sqrt { 3 } i , - 3 + 3 \sqrt { 3 } i$ 
D)  $\quad x = - 2 , - 216$ 
E)  $\quad x = 0,2,6$ 
A)  $x = 2,216$ 
B)  $x = 0 , - 2 , - 6$ 
C)  $\quad x = 0,2,6 , - 3 - 3 \sqrt { 3 } i , - 3 + 3 \sqrt { 3 } i$ 
D)  $\quad x = - 2 , - 216$ 
E)  $\quad x = 0,2,6$

Question 8

Determine the $x$-intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } - 10 x + 26$.

Accepted Answer

A)  $( 0,0 ) , ( 4,0 )$ 
B)  $( 5,0 ) , ( 10,0 )$ 
C)  $( 7,0 ) , ( 2,0 )$ 
D)  $( 0,0 ) , ( 2,0 )$ 
E)  no $x$-intercept(s) 
A)  $( 0,0 ) , ( 4,0 )$ 
B)  $( 5,0 ) , ( 10,0 )$ 
C)  $( 7,0 ) , ( 2,0 )$ 
D)  $( 0,0 ) , ( 2,0 )$ 
E)  no $x$-intercept(s)

Question 9

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 10

Find all the rational zeros of the function $f ( x ) = 3 x ^ { 4 } - 16 x ^ { 3 } - 59 x ^ { 2 } + 400 x - 400$.

Accepted Answer

A)  $x = - 4,5 , - 5 , - \frac { 3 } { 4 }$ 
B)  $x = 3 , - 20,5$ 
C)  $x = 4,5 , - 5 , \frac { 4 } { 3 }$ 
D)  $x = - \frac { 4 } { 5 } , \frac { 5 } { 3 } , \frac { 4 } { 3 } , - 5$ 
E)  $x = 3 , - 20 , \frac { 5 } { 3 } , \frac { 4 } { 3 }$ 
A)  $x = - 4,5 , - 5 , - \frac { 3 } { 4 }$ 
B)  $x = 3 , - 20,5$ 
C)  $x = 4,5 , - 5 , \frac { 4 } { 3 }$ 
D)  $x = - \frac { 4 } { 5 } , \frac { 5 } { 3 } , \frac { 4 } { 3 } , - 5$ 
E)  $x = 3 , - 20 , \frac { 5 } { 3 } , \frac { 4 } { 3 }$

Question 11

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form.
$1 + \sqrt { - 20 }$

Accepted Answer

A)  $1 - 20 i ; 19$ 
B)  $1 - 5 \sqrt { 2 } i ; 21$ 
C)  $- 1 - 2 \sqrt { 5 } i ; 21$ 
D)  $- 1 - 2 \sqrt { 5 } i ; 19$ 
E)  $1 - 2 \sqrt { 5 } i ; 21$ 
A)  $1 - 20 i ; 19$ 
B)  $1 - 5 \sqrt { 2 } i ; 21$ 
C)  $- 1 - 2 \sqrt { 5 } i ; 21$ 
D)  $- 1 - 2 \sqrt { 5 } i ; 19$ 
E)  $1 - 2 \sqrt { 5 } i ; 21$

Question 12

Match the equation with its graph.
$f ( x ) = x ^ { 2 } + 2 x - 3$

Accepted Answer

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

Question 13

The interest rates that banks charge to borrow money fluctuate with the economy. The interest rate charged by a bank in a certain country is given in the table below. Let $t$ represent the year, with $t = 0$ corresponding to 1986 . Use the regression feature of a graphing utility to find a quadratic model of the form
$\begin{array}{|c|c|}
\hline \begin{array}{c}
\text { Year } \
\boldsymbol{t}
\end{array} & \text { Percent } \
\hline \boldsymbol{y} \
\hline 1986 & 12.8 \
\hline 1988 & 10.0 \
\hline 1990 & 6.9 \
\hline 1992 & 5.7 \
\hline 1994 & 8.6 \
\hline 1996 & 12.7 \
\hline
\end{array}$

Accepted Answer

A)  $y = - 2.7 t ^ { 2 } + 13.35 t + 0.26$ 
B)  $y = 13.35 t ^ { 2 } + 0.26 t - 2.7$ 
C)  $y = 0.26 t ^ { 2 } - 2.7 t + 13.35$ 
D)  $y = 0.21 t ^ { 2 } - 3.26 t + 11.22$ 
E)  $y = 0.32 t ^ { 2 } - 2.18 t + 15.22$ 
A)  $y = - 2.7 t ^ { 2 } + 13.35 t + 0.26$ 
B)  $y = 13.35 t ^ { 2 } + 0.26 t - 2.7$ 
C)  $y = 0.26 t ^ { 2 } - 2.7 t + 13.35$ 
D)  $y = 0.21 t ^ { 2 } - 3.26 t + 11.22$ 
E)  $y = 0.32 t ^ { 2 } - 2.18 t + 15.22$

Question 14

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 200 .

Accepted Answer

A)  160,10 
B)  116,21 
C)  108,23 
D)  100,25 
E)  76,31 
A)  160,10 
B)  116,21 
C)  108,23 
D)  100,25 
E)  76,31

Question 15

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 16

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.
$\begin{array}{|c|c|}
\hline \text { IQ Score } & \text { Number of People } \
\boldsymbol{y} & \boldsymbol{x} \
\hline 70 & 53 \
\hline 80 & 72 \
\hline 90 & 93 \
\hline 100 & 90 \
\hline 110 & 78 \
\hline 120 & 47 \
\hline 130 & 16 \
\hline
\end{array}$

Accepted Answer

A)  $y = - 0.04 x ^ { 2 } + 14.93 x - 404.96$ 
B)  $y = - 0.06 x ^ { 2 } + 11.94 x - 476.43$ 
C)  $y = - 0.08 x ^ { 2 } + 10.87 x - 500.25$ 
D)  $y = - 0.07 x ^ { 2 } + 13.5 x - 452.61$ 
E)  $y = - 0.09 x ^ { 2 } + 8.48 x - 547.89$ 
A)  $y = - 0.04 x ^ { 2 } + 14.93 x - 404.96$ 
B)  $y = - 0.06 x ^ { 2 } + 11.94 x - 476.43$ 
C)  $y = - 0.08 x ^ { 2 } + 10.87 x - 500.25$ 
D)  $y = - 0.07 x ^ { 2 } + 13.5 x - 452.61$ 
E)  $y = - 0.09 x ^ { 2 } + 8.48 x - 547.89$

Question 17

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 18

Determine the $x$-intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } - 12 x + 37$.

Accepted Answer

A)  $( 1,0 ) , ( 9,0 )$ 
B)  $( 6,0 ) , ( 15,0 )$ 
C)  $( 8,0 ) , ( 3,0 )$ 
D)  $( 1,0 ) , ( 3,0 )$ 
E)  no $x$-intercept(s) 
A)  $( 1,0 ) , ( 9,0 )$ 
B)  $( 6,0 ) , ( 15,0 )$ 
C)  $( 8,0 ) , ( 3,0 )$ 
D)  $( 1,0 ) , ( 3,0 )$ 
E)  no $x$-intercept(s)

Question 19

Find the quadratic function $f$ whose graph intersects the $x$-axis at $( - 7,0 )$ and $( 1,0 )$ and the $y$-axis at $( 0 , - 14 )$.

Accepted Answer

A)  $f ( x ) = - 2 x ^ { 2 } - 16 x - 2$ 
B)  $f ( x ) = 2 x ^ { 2 } + 12 x - 14$ 
C)  $f ( x ) = 2 x ^ { 2 } + 16 x - 7$ 
D)  $f ( x ) = - 2 x ^ { 2 } + 16 x - 14$ 
E)  $f ( x ) = - 2 x ^ { 2 } - 12 x - 14$ 
A)  $f ( x ) = - 2 x ^ { 2 } - 16 x - 2$ 
B)  $f ( x ) = 2 x ^ { 2 } + 12 x - 14$ 
C)  $f ( x ) = 2 x ^ { 2 } + 16 x - 7$ 
D)  $f ( x ) = - 2 x ^ { 2 } + 16 x - 14$ 
E)  $f ( x ) = - 2 x ^ { 2 } - 12 x - 14$

Question 20

Which of the following is the graph of the given equation?
$f ( x ) = \frac { 2 - x } { x + 3 }$

Accepted Answer

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

A polynomial function $f$ has degree 3 , the zeros below, and a solution point of $f ( - 3 ) = - 4$ . Write $f$ in completely factored form. $- 4 , - 3 + 2 i$

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

Determine the $x$ -intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } - 15 x + 56$ .

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

Find real numbers $a$ and $b$ such that the equation $a + b i = - 10 + 10 i$ is true.

If $x = \frac { 2 } { 5 }$ is a root of $25 x ^ { 3 } - 70 x ^ { 2 } + 44 x - 8 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Find all zeros of the function $f ( x ) = x ^ { 2 } ( x - 2 ) \left( x ^ { 3 } - 216 \right)$ .

Determine the $x$ -intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } - 10 x + 26$ .

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

Find all the rational zeros of the function $f ( x ) = 3 x ^ { 4 } - 16 x ^ { 3 } - 59 x ^ { 2 } + 400 x - 400$ .

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form. $1 + \sqrt { - 20 }$

Match the equation with its graph. $f ( x ) = x ^ { 2 } + 2 x - 3$

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 200 .

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

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

Determine the $x$ -intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } - 12 x + 37$ .

Find the quadratic function $f$ whose graph intersects the $x$ -axis at $( - 7,0 )$ and $( 1,0 )$ and the $y$ -axis at $( 0 , - 14 )$ .

Which of the following is the graph of the given equation? $f ( x ) = \frac { 2 - x } { x + 3 }$

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

Filters

Exam 2: Polynomial and Rational Functions

A polynomial function fff has degree 3 , the zeros below, and a solution point of f(−3)=−4f ( - 3 ) = - 4f(−3)=−4 . Write fff in completely factored form. −4,−3+2i- 4 , - 3 + 2 i−4,−3+2i

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

Determine the xxx -intercept(s) of the quadratic function f(x)=x2−15x+56f ( x ) = x ^ { 2 } - 15 x + 56f(x)=x2−15x+56 .

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

Find real numbers aaa and bbb such that the equation a+bi=−10+10ia + b i = - 10 + 10 ia+bi=−10+10i is true.

If x=25x = \frac { 2 } { 5 }x=52​ is a root of 25x3−70x2+44x−8=025 x ^ { 3 } - 70 x ^ { 2 } + 44 x - 8 = 025x3−70x2+44x−8=0 , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Find all zeros of the function f(x)=x2(x−2)(x3−216)f ( x ) = x ^ { 2 } ( x - 2 ) \left( x ^ { 3 } - 216 \right)f(x)=x2(x−2)(x3−216) .

Determine the xxx -intercept(s) of the quadratic function f(x)=x2−10x+26f ( x ) = x ^ { 2 } - 10 x + 26f(x)=x2−10x+26 .

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) .

Find all the rational zeros of the function f(x)=3x4−16x3−59x2+400x−400f ( x ) = 3 x ^ { 4 } - 16 x ^ { 3 } - 59 x ^ { 2 } + 400 x - 400f(x)=3x4−16x3−59x2+400x−400 .

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form. 1+−201 + \sqrt { - 20 }1+−20​

Match the equation with its graph. f(x)=x2+2x−3f ( x ) = x ^ { 2 } + 2 x - 3f(x)=x2+2x−3

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 200 .

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

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

Determine the xxx -intercept(s) of the quadratic function f(x)=x2−12x+37f ( x ) = x ^ { 2 } - 12 x + 37f(x)=x2−12x+37 .

Find the quadratic function fff whose graph intersects the xxx -axis at (−7,0)( - 7,0 )(−7,0) and (1,0)( 1,0 )(1,0) and the yyy -axis at (0,−14)( 0 , - 14 )(0,−14) .

Which of the following is the graph of the given equation? f(x)=2−xx+3f ( x ) = \frac { 2 - x } { x + 3 }f(x)=x+32−x​

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

Filters

A polynomial function $f$ has degree 3 , the zeros below, and a solution point of $f ( - 3 ) = - 4$ . Write $f$ in completely factored form. $- 4 , - 3 + 2 i$

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

Determine the $x$ -intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } - 15 x + 56$ .

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

Find real numbers $a$ and $b$ such that the equation $a + b i = - 10 + 10 i$ is true.

If $x = \frac { 2 } { 5 }$ is a root of $25 x ^ { 3 } - 70 x ^ { 2 } + 44 x - 8 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Find all zeros of the function $f ( x ) = x ^ { 2 } ( x - 2 ) \left( x ^ { 3 } - 216 \right)$ .

Determine the $x$ -intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } - 10 x + 26$ .

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

Find all the rational zeros of the function $f ( x ) = 3 x ^ { 4 } - 16 x ^ { 3 } - 59 x ^ { 2 } + 400 x - 400$ .

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form. $1 + \sqrt { - 20 }$

Match the equation with its graph. $f ( x ) = x ^ { 2 } + 2 x - 3$

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

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

Determine the $x$ -intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } - 12 x + 37$ .

Find the quadratic function $f$ whose graph intersects the $x$ -axis at $( - 7,0 )$ and $( 1,0 )$ and the $y$ -axis at $( 0 , - 14 )$ .

Which of the following is the graph of the given equation? $f ( x ) = \frac { 2 - x } { x + 3 }$