Find a quadratic function that best fits the data. Give answers to the nearest hundredth. -$\begin{array}{c|c|c|c} x & -2 & 5 & 8 \\ \hline y & 5 & 7 & 14 \end{array}$

A) $y = 0.21 - 1.28 x + 6.44$ B) $y = 0.20 x ^ { 2 } - 0.33 x + 3.52$ C) $y = 0.20 x ^ { 2 } + 0.33 x + 3.52$ D) $y = - 0.13 x ^ { 2 } - 0.67 x + 6.86$ A) $y = 0.21 - 1.28 x + 6.44$ B) $y = 0.20 x ^ { 2 } - 0.33 x + 3.52$ C) $y = 0.20 x ^ { 2 } + 0.33 x + 3.52$ D) $y = - 0.13 x ^ { 2 } - 0.67 x + 6.86$

Find a power function that models the data in the table. Round to three decimal places if necessary. -$\begin{array}{c|ccccc} x & 2 & 4 & 6 & 8 & 10 \\ \hline y & 6.7 & 12.1 & 15.4 & 18.8 & 22.7 \end{array}$

A) $y = 1.935 x + 3.53$ B) $y = 0.742 x ^ { 4.104 }$ C) $y = 5.887 x ^ { 1.155 }$ D) $y = 4.104 x ^ { 0.742 }$ A) $y = 1.935 x + 3.53$ B) $y = 0.742 x ^ { 4.104 }$ C) $y = 5.887 x ^ { 1.155 }$ D) $y = 4.104 x ^ { 0.742 }$

Exam 3: Quadratic, Piecewise-Defined, and Power Functions

Provide an appropriate response. -Verify that the following data points give constant second differences. Does this guarantee that the points fit exactly on a quadratic function? Why or why not? x y 1 0 3 3 9 12 27 27 81 48

(Essay)

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Question 141

Does it appear that a linear model or a quadratic model is the best fit for the data given in the table below? Explain your choice. x y 2 25 4 110 6 258 8 472

(Essay)

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Question 142

Use factoring to solve the equation - $12 \mathrm {~d} ^ { 2 } + 38 \mathrm {~d} + 30 = 0$

(Multiple Choice)

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Question 143

Find a quadratic function that best fits the data. Give answers to the nearest hundredth. - x -2 5 8 y 5 7 14

(Multiple Choice)

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Question 144

Use the quadratic formula to - $4 n ^ { 2 } = - 8 n - 1$

(Multiple Choice)

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(32)

Question 145

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y = - x ^ { 2 } - 4 x - 3$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y = - x ^ { 2 } - 4 x - 3$

(Multiple Choice)

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(43)

Question 146

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y = x ^ { 2 } + 5$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y = x ^ { 2 } + 5$

(Multiple Choice)

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Question 147

A study in a small town showed that the percent of residents who have college degrees can be modeled by the function $P = 35 x ^ { 0.34 }$ where x is the number of years since 2010. Use numerical or graphical methods to find When the model predicts that the percent will be 70.

(Multiple Choice)

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Question 148

Provide an appropriate response. -If the points in the table lie on a parabola, write the equation whose graph is the parabola. 5 4 3 2 1 0 -24 -9 0 3 0 -9

(Multiple Choice)

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Question 149

Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function. - $y = x ^ { 2 } + 6 x + 8$

(Multiple Choice)

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Question 150

Determine if the function is increasing or decreasing over the interval indicated. - $y = - 6 x ^ { 3 } ; x < 0$

(Multiple Choice)

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Question 151

Assume it costs 30 cents to mail a letter weighing one ounce or less, and then 28 cents for each additional ounce or fraction of an ounce. Write a piecewise-defined function P(x) that represents the cost, in cents, of mailing a Letter weighing between 0 and 3 ounces.

(Multiple Choice)

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Question 152

The cumulative number (in thousands) of deaths from a certain disease from 2000 to 2010 may be modeled by $A = 2.39 x ^ { 2 } + 5.04 x + 5.1 , \text { where } x = 0 \text { corresponds to } 2000 , x = 1 \text { to } 2001$ , etc. Use the formula for A to estimate symbolically the year when the total number of deaths reached 150 thousand.

(Multiple Choice)

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Question 153

Write the equation of the quadratic function whose graph is a parabola containing the given points. - $( 0 , - 1 ) , ( 4,51 ) , ( - 2,9 )$

(Multiple Choice)

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Question 154

Find a power function that models the data in the table. Round to three decimal places if necessary. - x 2 4 6 8 10 y 6.7 12.1 15.4 18.8 22.7

(Multiple Choice)

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(32)

Question 155

Use the graph of the function to estimate the x-intercepts. - $g(x)=-8 x^{2}+18 x+5$ $Use the graph of the function to estimate the x-intercepts. - g(x)=-8 x^{2}+18 x+5$

(Multiple Choice)

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Question 156

Determine if the graph of the function is concave up or concave down - $g ( x ) = ( x - 3 ) ^ { 2 } + 2$

(Multiple Choice)

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Question 157

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $x ^ { 2 } + 5 x = - 3$

(Multiple Choice)

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Question 158

Use the quadratic formula to - $2 x ^ { 2 } - 16 x + 30 = 0$

(Multiple Choice)

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Question 159

A manufacturer has found that the daily demand for a certain item is $\frac { 300 } { p }$ , where $p$ is the price of the item in dollars. The daily supply is $6 \mathrm { p } - 3$ . At what price does supply equal demand? Round your answer to the nearest cent.

(Multiple Choice)

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Question 160

Provide an appropriate response. -Verify that the following data points give constant second differences. Does this guarantee that the points fit exactly on a quadratic function? Why or why not? x y 1 0 3 3 9 12 27 27 81 48

Does it appear that a linear model or a quadratic model is the best fit for the data given in the table below? Explain your choice. x y 2 25 4 110 6 258 8 472

Use factoring to solve the equation - $12 \mathrm {~d} ^ { 2 } + 38 \mathrm {~d} + 30 = 0$

Find a quadratic function that best fits the data. Give answers to the nearest hundredth. - x -2 5 8 y 5 7 14

Use the quadratic formula to - $4 n ^ { 2 } = - 8 n - 1$

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y = - x ^ { 2 } - 4 x - 3$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y = - x ^ { 2 } - 4 x - 3$

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y = x ^ { 2 } + 5$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y = x ^ { 2 } + 5$

A study in a small town showed that the percent of residents who have college degrees can be modeled by the function $P = 35 x ^ { 0.34 }$ where x is the number of years since 2010. Use numerical or graphical methods to find When the model predicts that the percent will be 70.

Provide an appropriate response. -If the points in the table lie on a parabola, write the equation whose graph is the parabola. 5 4 3 2 1 0 -24 -9 0 3 0 -9

Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function. - $y = x ^ { 2 } + 6 x + 8$

Determine if the function is increasing or decreasing over the interval indicated. - $y = - 6 x ^ { 3 } ; x < 0$

Assume it costs 30 cents to mail a letter weighing one ounce or less, and then 28 cents for each additional ounce or fraction of an ounce. Write a piecewise-defined function P(x) that represents the cost, in cents, of mailing a Letter weighing between 0 and 3 ounces.

Write the equation of the quadratic function whose graph is a parabola containing the given points. - $( 0 , - 1 ) , ( 4,51 ) , ( - 2,9 )$

Find a power function that models the data in the table. Round to three decimal places if necessary. - x 2 4 6 8 10 y 6.7 12.1 15.4 18.8 22.7

Use the graph of the function to estimate the x-intercepts. - $g(x)=-8 x^{2}+18 x+5$ $Use the graph of the function to estimate the x-intercepts. - g(x)=-8 x^{2}+18 x+5$

Determine if the graph of the function is concave up or concave down - $g ( x ) = ( x - 3 ) ^ { 2 } + 2$

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $x ^ { 2 } + 5 x = - 3$

Use the quadratic formula to - $2 x ^ { 2 } - 16 x + 30 = 0$

A manufacturer has found that the daily demand for a certain item is $\frac { 300 } { p }$ , where $p$ is the price of the item in dollars. The daily supply is $6 \mathrm { p } - 3$ . At what price does supply equal demand? Round your answer to the nearest cent.

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Exam 3: Quadratic, Piecewise-Defined, and Power Functions

Provide an appropriate response. -Verify that the following data points give constant second differences. Does this guarantee that the points fit exactly on a quadratic function? Why or why not? x y 1 0 3 3 9 12 27 27 81 48

Does it appear that a linear model or a quadratic model is the best fit for the data given in the table below? Explain your choice. x y 2 25 4 110 6 258 8 472

Use factoring to solve the equation - 12 d2+38 d+30=012 \mathrm {~d} ^ { 2 } + 38 \mathrm {~d} + 30 = 012 d2+38 d+30=0

Find a quadratic function that best fits the data. Give answers to the nearest hundredth. - x -2 5 8 y 5 7 14

Use the quadratic formula to - 4n2=−8n−14 n ^ { 2 } = - 8 n - 14n2=−8n−1

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=−x2−4x−3y = - x ^ { 2 } - 4 x - 3y=−x2−4x−3

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y=x2+5y = x ^ { 2 } + 5y=x2+5

A study in a small town showed that the percent of residents who have college degrees can be modeled by the function P=35x0.34P = 35 x ^ { 0.34 }P=35x0.34 where x is the number of years since 2010. Use numerical or graphical methods to find When the model predicts that the percent will be 70.

Provide an appropriate response. -If the points in the table lie on a parabola, write the equation whose graph is the parabola. 5 4 3 2 1 0 -24 -9 0 3 0 -9

Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function. - y=x2+6x+8y = x ^ { 2 } + 6 x + 8y=x2+6x+8

Determine if the function is increasing or decreasing over the interval indicated. - y=−6x3;x<0y = - 6 x ^ { 3 } ; x < 0y=−6x3;x<0

Assume it costs 30 cents to mail a letter weighing one ounce or less, and then 28 cents for each additional ounce or fraction of an ounce. Write a piecewise-defined function P(x) that represents the cost, in cents, of mailing a Letter weighing between 0 and 3 ounces.

Write the equation of the quadratic function whose graph is a parabola containing the given points. - (0,−1),(4,51),(−2,9)( 0 , - 1 ) , ( 4,51 ) , ( - 2,9 )(0,−1),(4,51),(−2,9)

Find a power function that models the data in the table. Round to three decimal places if necessary. - x 2 4 6 8 10 y 6.7 12.1 15.4 18.8 22.7

Use the graph of the function to estimate the x-intercepts. - g(x)=−8x2+18x+5g(x)=-8 x^{2}+18 x+5g(x)=−8x2+18x+5

Determine if the graph of the function is concave up or concave down - g(x)=(x−3)2+2g ( x ) = ( x - 3 ) ^ { 2 } + 2g(x)=(x−3)2+2

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - x2+5x=−3x ^ { 2 } + 5 x = - 3x2+5x=−3

Use the quadratic formula to - 2x2−16x+30=02 x ^ { 2 } - 16 x + 30 = 02x2−16x+30=0

A manufacturer has found that the daily demand for a certain item is 300p\frac { 300 } { p }p300​ , where ppp is the price of the item in dollars. The daily supply is 6p−36 \mathrm { p } - 36p−3 . At what price does supply equal demand? Round your answer to the nearest cent.

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Use factoring to solve the equation - $12 \mathrm {~d} ^ { 2 } + 38 \mathrm {~d} + 30 = 0$

Use the quadratic formula to - $4 n ^ { 2 } = - 8 n - 1$

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y = - x ^ { 2 } - 4 x - 3$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y = - x ^ { 2 } - 4 x - 3$

Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - $y = x ^ { 2 } + 5$ $Give the coordinates of the vertex and graph the equation in a window that includes the vertex. - y = x ^ { 2 } + 5$

A study in a small town showed that the percent of residents who have college degrees can be modeled by the function $P = 35 x ^ { 0.34 }$ where x is the number of years since 2010. Use numerical or graphical methods to find When the model predicts that the percent will be 70.

Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function. - $y = x ^ { 2 } + 6 x + 8$

Determine if the function is increasing or decreasing over the interval indicated. - $y = - 6 x ^ { 3 } ; x < 0$

Write the equation of the quadratic function whose graph is a parabola containing the given points. - $( 0 , - 1 ) , ( 4,51 ) , ( - 2,9 )$

Use the graph of the function to estimate the x-intercepts. - $g(x)=-8 x^{2}+18 x+5$ $Use the graph of the function to estimate the x-intercepts. - g(x)=-8 x^{2}+18 x+5$

Determine if the graph of the function is concave up or concave down - $g ( x ) = ( x - 3 ) ^ { 2 } + 2$

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $x ^ { 2 } + 5 x = - 3$

Use the quadratic formula to - $2 x ^ { 2 } - 16 x + 30 = 0$

A manufacturer has found that the daily demand for a certain item is $\frac { 300 } { p }$ , where $p$ is the price of the item in dollars. The daily supply is $6 \mathrm { p } - 3$ . At what price does supply equal demand? Round your answer to the nearest cent.