Use the regression feature of a graphing utility to find a quadratic model for the data below. $\begin{array}{|r|c|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline-2 & -7.3 \\ \hline-1 & -2 \\ \hline 0 & -1 \\ \hline 1 & -4.8 \\ \hline 2 & -11.4 \\ \hline 3 & -22.8 \\ \hline 4 & -37.8 \\ \hline \end{array}$

A) $y = - 1.91 x ^ { 2 } - 1.21 x - 1.57$ B) $y = - 1.81 x ^ { 2 } - 1.15 x - 1.42$ C) $y = - 2.21 x ^ { 2 } - 1.04 x - 1$ D) $y = - 2.11 x ^ { 2 } - 0.99 x - 1.07$ E) $y = - 2.01 x ^ { 2 } - 1.1 x - 1.28$ A) $y = - 1.91 x ^ { 2 } - 1.21 x - 1.57$ B) $y = - 1.81 x ^ { 2 } - 1.15 x - 1.42$ C) $y = - 2.21 x ^ { 2 } - 1.04 x - 1$ D) $y = - 2.11 x ^ { 2 } - 0.99 x - 1.07$ E) $y = - 2.01 x ^ { 2 } - 1.1 x - 1.28$

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. $\begin{array}{|c|c|} \hline \text { IQ Score } & \text { Number of People } \\ \boldsymbol{y} & \boldsymbol{x} \\ \hline 70 & 50 \\ \hline 80 & 76 \\ \hline 90 & 89 \\ \hline 100 & 93 \\ \hline 110 & 74 \\ \hline 120 & 53 \\ \hline 130 & 16 \\ \hline \end{array}$

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) $y = - 0.09 x ^ { 2 } + 8.56 x - 556.85$

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

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) $y = 3.04 x ^ { 2 } - 3.05 x - 2.61$

Exam 2: Polynomial and Rational Functions

Find a polynomial function with following characteristics. Degree: 4 Zero: 4 , multiplicity: 2 Zero: $- 3$ , multiplicity: 2 Falls to the left, Falls to the right Absolute value of the leading coefficient is one

(Multiple Choice)

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Question 41

Use the regression feature of a graphing utility to find a quadratic model for the data below. -2 -7.3 -1 -2 0 -1 1 -4.8 2 -11.4 3 -22.8 4 -37.8

(Multiple Choice)

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(64)

Question 42

Write $f ( x ) = x ^ { 3 } - 11 x ^ { 2 } + 18 x + 25$ in the form $f ( x ) = ( x - k ) q ( x ) + r$ when $k = 6 + \sqrt { 6 }$ .

(Multiple Choice)

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(76)

Question 43

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } - x + \frac { 5 } { 4 }$ .

(Multiple Choice)

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Question 44

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form. $2 + \sqrt { - 27 }$

(Multiple Choice)

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(85)

Question 45

Identify any horizontal and vertical asymptotes of the function below. $f ( x ) = \frac { 2 x - 8 } { | x | + 6 }$

(Multiple Choice)

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Question 46

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. IQ Score Number of People 70 50 80 76 90 89 100 93 110 74 120 53 130 16

(Multiple Choice)

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(62)

Question 47

Use long division to divide. $\left( x ^ { 3 } + 27 \right) \div ( x + 3 )$

(Multiple Choice)

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(78)

Question 48

Simplify $f$ below and find any vertical asymptotes of $f$ . $f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$

(Multiple Choice)

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(80)

Question 49

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

(Multiple Choice)

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Question 50

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

(Multiple Choice)

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Question 51

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$ .

(Multiple Choice)

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(90)

Question 52

If $x = 4$ is a root of $x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

(Multiple Choice)

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Question 53

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. $0,2,4 - i$

(Multiple Choice)

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Question 54

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } - 80 x ^ { 2 } + 1024$ and determine the mutiplicity of each.

(Multiple Choice)

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(71)

Question 55

Compare the graph of $p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9$ with $p ( x ) = x ^ { 2 }$ .

(Multiple Choice)

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Question 56

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$ and determine the mutiplicity of each.

(Multiple Choice)

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(68)

Question 57

Which of the given graphs is the graph of the polynomial function below? $h ( x ) = x ^ { 5 } + \frac { 3 } { 2 } x ^ { 3 } - \frac { 1 } { 2 } x$ Graph 1 : $Which of the given graphs is the graph of the polynomial function below? h ( x ) = x ^ { 5 } + \frac { 3 } { 2 } x ^ { 3 } - \frac { 1 } { 2 } x Graph 1 : Graph 2: Graph 3 : Graph 4 : Graph 5 :$ Graph 2: $Which of the given graphs is the graph of the polynomial function below? h ( x ) = x ^ { 5 } + \frac { 3 } { 2 } x ^ { 3 } - \frac { 1 } { 2 } x Graph 1 : Graph 2: Graph 3 : Graph 4 : Graph 5 :$ Graph 3 : $Which of the given graphs is the graph of the polynomial function below? h ( x ) = x ^ { 5 } + \frac { 3 } { 2 } x ^ { 3 } - \frac { 1 } { 2 } x Graph 1 : Graph 2: Graph 3 : Graph 4 : Graph 5 :$ Graph 4 : $Which of the given graphs is the graph of the polynomial function below? h ( x ) = x ^ { 5 } + \frac { 3 } { 2 } x ^ { 3 } - \frac { 1 } { 2 } x Graph 1 : Graph 2: Graph 3 : Graph 4 : Graph 5 :$ Graph 5 : $Which of the given graphs is the graph of the polynomial function below? h ( x ) = x ^ { 5 } + \frac { 3 } { 2 } x ^ { 3 } - \frac { 1 } { 2 } x Graph 1 : Graph 2: Graph 3 : Graph 4 : Graph 5 :$

(Multiple Choice)

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Question 58

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 9 } { x - 2 }$ .

(Multiple Choice)

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Question 59

If $x = - 1$ is a root of $x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

(Multiple Choice)

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Question 60

Showing 41 - 60 of 120

Find a polynomial function with following characteristics. Degree: 4 Zero: 4 , multiplicity: 2 Zero: $- 3$ , multiplicity: 2 Falls to the left, Falls to the right Absolute value of the leading coefficient is one

Use the regression feature of a graphing utility to find a quadratic model for the data below. -2 -7.3 -1 -2 0 -1 1 -4.8 2 -11.4 3 -22.8 4 -37.8

Write $f ( x ) = x ^ { 3 } - 11 x ^ { 2 } + 18 x + 25$ in the form $f ( x ) = ( x - k ) q ( x ) + r$ when $k = 6 + \sqrt { 6 }$ .

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } - x + \frac { 5 } { 4 }$ .

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form. $2 + \sqrt { - 27 }$

Identify any horizontal and vertical asymptotes of the function below. $f ( x ) = \frac { 2 x - 8 } { | x | + 6 }$

Use long division to divide. $\left( x ^ { 3 } + 27 \right) \div ( x + 3 )$

Simplify $f$ below and find any vertical asymptotes of $f$ . $f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$

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

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

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$ .

If $x = 4$ is a root of $x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. $0,2,4 - i$

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } - 80 x ^ { 2 } + 1024$ and determine the mutiplicity of each.

Compare the graph of $p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9$ with $p ( x ) = x ^ { 2 }$ .

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$ and determine the mutiplicity of each.

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 9 } { x - 2 }$ .

If $x = - 1$ is a root of $x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

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

Find a polynomial function with following characteristics. Degree: 4 Zero: 4 , multiplicity: 2 Zero: −3- 3−3 , multiplicity: 2 Falls to the left, Falls to the right Absolute value of the leading coefficient is one

Use the regression feature of a graphing utility to find a quadratic model for the data below. -2 -7.3 -1 -2 0 -1 1 -4.8 2 -11.4 3 -22.8 4 -37.8

Write f(x)=x3−11x2+18x+25f ( x ) = x ^ { 3 } - 11 x ^ { 2 } + 18 x + 25f(x)=x3−11x2+18x+25 in the form f(x)=(x−k)q(x)+rf ( x ) = ( x - k ) q ( x ) + rf(x)=(x−k)q(x)+r when k=6+6k = 6 + \sqrt { 6 }k=6+6​ .

Determine the vertex of the graph of the quadratic function f(x)=x2−x+54f ( x ) = x ^ { 2 } - x + \frac { 5 } { 4 }f(x)=x2−x+45​ .

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form. 2+−272 + \sqrt { - 27 }2+−27​

Identify any horizontal and vertical asymptotes of the function below. f(x)=2x−8∣x∣+6f ( x ) = \frac { 2 x - 8 } { | x | + 6 }f(x)=∣x∣+62x−8​

Use long division to divide. (x3+27)÷(x+3)\left( x ^ { 3 } + 27 \right) \div ( x + 3 )(x3+27)÷(x+3)

Simplify fff below and find any vertical asymptotes of fff . f(x)=x2−25x+5f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }f(x)=x+5x2−25​

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

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

Determine the vertex of the graph of the quadratic function f(x)=x2+5x+294f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }f(x)=x2+5x+429​ .

If x=4x = 4x=4 is a root of x3+5x2−16x−80=0x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0x3+5x2−16x−80=0 , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. 0,2,4−i0,2,4 - i0,2,4−i

Find all real zeros of the polynomial f(x)=x4−80x2+1024f ( x ) = x ^ { 4 } - 80 x ^ { 2 } + 1024f(x)=x4−80x2+1024 and determine the mutiplicity of each.

Compare the graph of p(x)=[−13(x+9)]2−9p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9p(x)=[−31​(x+9)]2−9 with p(x)=x2p ( x ) = x ^ { 2 }p(x)=x2 .

Find all real zeros of the polynomial f(x)=x4+8x3+12x2f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }f(x)=x4+8x3+12x2 and determine the mutiplicity of each.

Which of the given graphs is the graph of the polynomial function below? h(x)=x5+32x3−12xh ( x ) = x ^ { 5 } + \frac { 3 } { 2 } x ^ { 3 } - \frac { 1 } { 2 } xh(x)=x5+23​x3−21​x Graph 1 : Graph 2: Graph 3 : Graph 4 : Graph 5 :

Determine the zeros (if any) of the rational function f(x)=x2−9x−2f ( x ) = \frac { x ^ { 2 } - 9 } { x - 2 }f(x)=x−2x2−9​ .

If x=−1x = - 1x=−1 is a root of x3+2x2−x−2=0x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0x3+2x2−x−2=0 , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

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

Find a polynomial function with following characteristics. Degree: 4 Zero: 4 , multiplicity: 2 Zero: $- 3$ , multiplicity: 2 Falls to the left, Falls to the right Absolute value of the leading coefficient is one

Write $f ( x ) = x ^ { 3 } - 11 x ^ { 2 } + 18 x + 25$ in the form $f ( x ) = ( x - k ) q ( x ) + r$ when $k = 6 + \sqrt { 6 }$ .

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } - x + \frac { 5 } { 4 }$ .

Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form. $2 + \sqrt { - 27 }$

Identify any horizontal and vertical asymptotes of the function below. $f ( x ) = \frac { 2 x - 8 } { | x | + 6 }$

Use long division to divide. $\left( x ^ { 3 } + 27 \right) \div ( x + 3 )$

Simplify $f$ below and find any vertical asymptotes of $f$ . $f ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$

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

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$ .

If $x = 4$ is a root of $x ^ { 3 } + 5 x ^ { 2 } - 16 x - 80 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. $0,2,4 - i$

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } - 80 x ^ { 2 } + 1024$ and determine the mutiplicity of each.

Compare the graph of $p ( x ) = \left[ - \frac { 1 } { 3 } ( x + 9 ) \right] ^ { 2 } - 9$ with $p ( x ) = x ^ { 2 }$ .

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$ and determine the mutiplicity of each.

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 9 } { x - 2 }$ .

If $x = - 1$ is a root of $x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.