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

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) $y = 2.01 x ^ { 2 } + 0.97 x + 3.44$

Exam 2: Polynomial and Rational Functions

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 Year Percent 1986 12.1 1988 10.1 1990 6.8 1992 6.6 1994 8.6 1996 12.0

(Multiple Choice)

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Question 81

Simplify $( \sqrt { - 3 } ) ^ { 9 }$ and write the answer in standard form.

(Multiple Choice)

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(85)

Question 82

Find real numbers $a$ and $b$ such that the equation $a + b i = 10 - 12 i$ is true.

(Multiple Choice)

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Question 83

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

(Multiple Choice)

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Question 84

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 $( 3 , - 4 )$ .

(Multiple Choice)

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Question 85

Find the zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 4 } + 8 x ^ { 2 } + 15$

(Multiple Choice)

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Question 86

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

(Multiple Choice)

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Question 87

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

(Multiple Choice)

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Question 88

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 13 x ^ { 3 } + 40 x ^ { 2 }$ and determine the mutiplicity of each.

(Multiple Choice)

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Question 89

Find the zeros of the function below algebraically, if any exist. $f ( x ) = 25 x ^ { 3 } - 60 x ^ { 2 } + 36 x$

(Multiple Choice)

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Question 90

Use synthetic division to divide. $\left( 6 + 5 x ^ { 3 } + 23 x + 22 x ^ { 2 } \right) \div ( x + 3 )$

(Multiple Choice)

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Question 91

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 49 x - 147$ and determine the mutiplicity of each.

(Multiple Choice)

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Question 92

Determine the domain of $f ( x ) = \frac { 3 x + 3 } { x ^ { 2 } - 3 x }$ .

(Multiple Choice)

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Question 93

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

(Multiple Choice)

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Question 94

A polynomial function $f$ has degree 3 , the zeros below, and a solution point of $f ( 1 ) = - 96$ . Write $f$ in completely factored form. $- 2 , - 3 + 4 i$

(Multiple Choice)

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Question 95

Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 2 } { x ^ { 2 } + 5 }$ .

(Multiple Choice)

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Question 96

Using the factors $( - 5 x + 2 )$ and $( x - 1 )$ , find the remaining factor(s) of $f ( x ) = 10 x ^ { 4 } + 31 x ^ { 3 } - 84 x ^ { 2 } + 53 x - 10$ and write the polynomial in fully factored form.

(Multiple Choice)

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Question 97

Perform the addition or subtraction and write the result in standard form. $- ( 7.2 - 12.3 i ) - ( 8.1 - \sqrt { - 1.21 } )$

(Multiple Choice)

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Question 98

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. $0 , - 3,1 + 3 i$

(Multiple Choice)

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(92)

Question 99

If If $f ( x ) = 4 x ^ { 2 } - 2 x - 7$ , use synthetic division to evaluate $f \left( \frac { 7 } { 8 } \right)$

(Multiple Choice)

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(83)

Question 100

Simplify $( \sqrt { - 3 } ) ^ { 9 }$ and write the answer in standard form.

Find real numbers $a$ and $b$ such that the equation $a + b i = 10 - 12 i$ is true.

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

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 zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 4 } + 8 x ^ { 2 } + 15$

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

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

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 13 x ^ { 3 } + 40 x ^ { 2 }$ and determine the mutiplicity of each.

Find the zeros of the function below algebraically, if any exist. $f ( x ) = 25 x ^ { 3 } - 60 x ^ { 2 } + 36 x$

Use synthetic division to divide. $\left( 6 + 5 x ^ { 3 } + 23 x + 22 x ^ { 2 } \right) \div ( x + 3 )$

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 49 x - 147$ and determine the mutiplicity of each.

Determine the domain of $f ( x ) = \frac { 3 x + 3 } { x ^ { 2 } - 3 x }$ .

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

A polynomial function $f$ has degree 3 , the zeros below, and a solution point of $f ( 1 ) = - 96$ . Write $f$ in completely factored form. $- 2 , - 3 + 4 i$

Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 2 } { x ^ { 2 } + 5 }$ .

Using the factors $( - 5 x + 2 )$ and $( x - 1 )$ , find the remaining factor(s) of $f ( x ) = 10 x ^ { 4 } + 31 x ^ { 3 } - 84 x ^ { 2 } + 53 x - 10$ and write the polynomial in fully factored form.

Perform the addition or subtraction and write the result in standard form. $- ( 7.2 - 12.3 i ) - ( 8.1 - \sqrt { - 1.21 } )$

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. $0 , - 3,1 + 3 i$

If If $f ( x ) = 4 x ^ { 2 } - 2 x - 7$ , use synthetic division to evaluate $f \left( \frac { 7 } { 8 } \right)$

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

Simplify (−3)9( \sqrt { - 3 } ) ^ { 9 }(−3​)9 and write the answer in standard form.

Find real numbers aaa and bbb such that the equation a+bi=10−12ia + b i = 10 - 12 ia+bi=10−12i is true.

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

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 zeros of the function below algebraically, if any exist. f(x)=x4+8x2+15f ( x ) = x ^ { 4 } + 8 x ^ { 2 } + 15f(x)=x4+8x2+15

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

Use long division to divide. (x3+3x2+x+3)÷(x+3)\left( x ^ { 3 } + 3 x ^ { 2 } + x + 3 \right) \div ( x + 3 )(x3+3x2+x+3)÷(x+3)

Find all real zeros of the polynomial f(x)=x4+13x3+40x2f ( x ) = x ^ { 4 } + 13 x ^ { 3 } + 40 x ^ { 2 }f(x)=x4+13x3+40x2 and determine the mutiplicity of each.

Find the zeros of the function below algebraically, if any exist. f(x)=25x3−60x2+36xf ( x ) = 25 x ^ { 3 } - 60 x ^ { 2 } + 36 xf(x)=25x3−60x2+36x

Use synthetic division to divide. (6+5x3+23x+22x2)÷(x+3)\left( 6 + 5 x ^ { 3 } + 23 x + 22 x ^ { 2 } \right) \div ( x + 3 )(6+5x3+23x+22x2)÷(x+3)

Find all real zeros of the polynomial f(x)=x3+3x2−49x−147f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 49 x - 147f(x)=x3+3x2−49x−147 and determine the mutiplicity of each.

Determine the domain of f(x)=3x+3x2−3xf ( x ) = \frac { 3 x + 3 } { x ^ { 2 } - 3 x }f(x)=x2−3x3x+3​ .

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

A polynomial function fff has degree 3 , the zeros below, and a solution point of f(1)=−96f ( 1 ) = - 96f(1)=−96 . Write fff in completely factored form. −2,−3+4i- 2 , - 3 + 4 i−2,−3+4i

Determine the zeros (if any) of the rational function g(x)=5+2x2+5g ( x ) = 5 + \frac { 2 } { x ^ { 2 } + 5 }g(x)=5+x2+52​ .

Using the factors (−5x+2)( - 5 x + 2 )(−5x+2) and (x−1)( x - 1 )(x−1) , find the remaining factor(s) of f(x)=10x4+31x3−84x2+53x−10f ( x ) = 10 x ^ { 4 } + 31 x ^ { 3 } - 84 x ^ { 2 } + 53 x - 10f(x)=10x4+31x3−84x2+53x−10 and write the polynomial in fully factored form.

Perform the addition or subtraction and write the result in standard form. −(7.2−12.3i)−(8.1−−1.21)- ( 7.2 - 12.3 i ) - ( 8.1 - \sqrt { - 1.21 } )−(7.2−12.3i)−(8.1−−1.21​)

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. 0,−3,1+3i0 , - 3,1 + 3 i0,−3,1+3i

If If f(x)=4x2−2x−7f ( x ) = 4 x ^ { 2 } - 2 x - 7f(x)=4x2−2x−7 , use synthetic division to evaluate f(78)f \left( \frac { 7 } { 8 } \right)f(87​)

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

Simplify $( \sqrt { - 3 } ) ^ { 9 }$ and write the answer in standard form.

Find real numbers $a$ and $b$ such that the equation $a + b i = 10 - 12 i$ is true.

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

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 zeros of the function below algebraically, if any exist. $f ( x ) = x ^ { 4 } + 8 x ^ { 2 } + 15$

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

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

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 13 x ^ { 3 } + 40 x ^ { 2 }$ and determine the mutiplicity of each.

Find the zeros of the function below algebraically, if any exist. $f ( x ) = 25 x ^ { 3 } - 60 x ^ { 2 } + 36 x$

Use synthetic division to divide. $\left( 6 + 5 x ^ { 3 } + 23 x + 22 x ^ { 2 } \right) \div ( x + 3 )$

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 49 x - 147$ and determine the mutiplicity of each.

Determine the domain of $f ( x ) = \frac { 3 x + 3 } { x ^ { 2 } - 3 x }$ .

A polynomial function $f$ has degree 3 , the zeros below, and a solution point of $f ( 1 ) = - 96$ . Write $f$ in completely factored form. $- 2 , - 3 + 4 i$

Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 2 } { x ^ { 2 } + 5 }$ .

Using the factors $( - 5 x + 2 )$ and $( x - 1 )$ , find the remaining factor(s) of $f ( x ) = 10 x ^ { 4 } + 31 x ^ { 3 } - 84 x ^ { 2 } + 53 x - 10$ and write the polynomial in fully factored form.

Perform the addition or subtraction and write the result in standard form. $- ( 7.2 - 12.3 i ) - ( 8.1 - \sqrt { - 1.21 } )$

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one. $0 , - 3,1 + 3 i$

If If $f ( x ) = 4 x ^ { 2 } - 2 x - 7$ , use synthetic division to evaluate $f \left( \frac { 7 } { 8 } \right)$