Find a power function that models the data in the table. Round to three decimal places if necessary. -A furniture manufacturer decides to make a new line of desks. The table shows the profit, in thousands of dollars, for various levels of production. \[\begin{array} { c | c c c c c } \begin{array} { c } \text { Number of } \\ \text { Desks Produced } \end{array} & 120 & 350 & 500 & 650 & 750 \\ \hline \text { Profit (Thousands) } & 13 & 37 & 44 & 34 & 25 \end{array}\] Find a quadratic function to model the data, and use the model to predict the profit if 450 desks are made. Round to the Nearest thousand.

A) $40,000 B) $42,000 C) $45,000 D) $44,000 A) $40,000 B) $42,000 C) $45,000 D) $44,000

Find a quadratic function that best fits the data. Give answers to the nearest hundredth. -$\begin{array}{c|c|c|c|c} \mathrm{x} & 2 & 34 & 79 & 110 \\ \hline \mathrm{y} & 1024 & 2345 & 2267 & 984 \end{array}$

A) $y = 0.54 x ^ { 2 } + 60.05 x + 912.48$ B) $y = - 0.7803 + 98.39 x - 419.89$ C) $y = - 0.54 x ^ { 2 } + 60.05 x + 912.48$ D) $y = - 4.66 x ^ { 2 } - 45.67 x + 345.67$ A) $y = 0.54 x ^ { 2 } + 60.05 x + 912.48$ B) $y = - 0.7803 + 98.39 x - 419.89$ C) $y = - 0.54 x ^ { 2 } + 60.05 x + 912.48$ D) $y = - 4.66 x ^ { 2 } - 45.67 x + 345.67$

Find a power function that models the data in the table. Round to three decimal places if necessary. -The height of a projectile moving vertically is given by the table, where t is the elapsed time in seconds and h is the height in feet. $\begin{array}{r|rrrrrr} \mathrm{t} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \mathrm{h} & 100 & 684 & 1236 & 1756 & 2244 & 2700 \end{array}$ If the height is modeled by $h ( t ) = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 }$, where $v _ { 0 }$ and $h _ { 0 }$ are the velocity and height at $t = 0$, respectively, find $\mathrm { v } _ { 0 }$.

A) $700 \mathrm { ft } / \mathrm { sec }$ B) $600 \mathrm { ft } / \mathrm { sec }$ C) $1200 \mathrm { ft } / \mathrm { sec }$ D) $350 \mathrm { ft } / \mathrm { sec }$ A) $700 \mathrm { ft } / \mathrm { sec }$ B) $600 \mathrm { ft } / \mathrm { sec }$ C) $1200 \mathrm { ft } / \mathrm { sec }$ D) $350 \mathrm { ft } / \mathrm { sec }$

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

Graph the function. - $f(x)=\left\{\begin{array}{l}4 x+1, \text { if } x<0 \\3 x^{2}-2, \text { if } x \geq 0\end{array}\right.$ $Graph the function. - f(x)=\left\{\begin{array}{l} 4 x+1, \text { if } x<0 \\ 3 x^{2}-2, \text { if } x \geq 0 \end{array}\right.$

(Multiple Choice)

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Question 121

The polynomial function $\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.4 \mathrm { t }$ represents the yearly income (or loss) from a real estate investment, where t is time in years. After how many years does income begin to decline?

(Multiple Choice)

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Question 122

Use the graph of the function to estimate the x-intercepts. - $g(x)=2 x^{2}+5 x-3$ $Use the graph of the function to estimate the x-intercepts. - g(x)=2 x^{2}+5 x-3$

(Multiple Choice)

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Question 123

Use the graph of the function to estimate the x-intercepts. - $y=x^{2}-x-6$ $Use the graph of the function to estimate the x-intercepts. - y=x^{2}-x-6$

(Multiple Choice)

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Question 124

Find a power function that models the data in the table. Round to three decimal places if necessary. -A furniture manufacturer decides to make a new line of desks. The table shows the profit, in thousands of dollars, for various levels of production. Number of Desks Produced 120 350 500 650 750 Profit (Thousands) 13 37 44 34 25 Find a quadratic function to model the data, and use the model to predict the profit if 450 desks are made. Round to the Nearest thousand.

(Multiple Choice)

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Question 125

Find a quadratic function that best fits the data. Give answers to the nearest hundredth. - 2 34 79 110 1024 2345 2267 984

(Multiple Choice)

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Question 126

The profit for a product is given by $\mathrm { p } = 2204 + \mathrm { x } ^ { 2 } - 105 \mathrm { x }$ x, where x is the number of units produced and sold. Graphically find the x-intercepts of this function to find how many units will give break-even (that is return a Profit of zero).

(Multiple Choice)

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Question 127

Determine if the function is increasing or decreasing over the interval indicated. - $y = - 8 x ^ { 4 } ; x < 0$

(Multiple Choice)

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Question 128

Use the square root method to - $8 z ^ { 2 } - 1568 = 0$

(Multiple Choice)

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Question 129

Determine if the vertex of the graph is a maximum point or a minimum point. - $g ( x ) = ( x - 1 ) ^ { 2 } + 5$

(Multiple Choice)

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Question 130

$- 6 x ^ { 2 } - 7 x - 6 = 0$

(Multiple Choice)

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Question 131

Find a power function that models the data in the table. Round to three decimal places if necessary. -The height of a projectile moving vertically is given by the table, where t is the elapsed time in seconds and h is the height in feet. 0 1 2 3 4 5 100 684 1236 1756 2244 2700 If the height is modeled by $h ( t ) = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 }$ , where $v _ { 0 }$ and $h _ { 0 }$ are the velocity and height at $t = 0$ , respectively, find $\mathrm { v } _ { 0 }$ .

(Multiple Choice)

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Question 132

Provide an appropriate response. -Which method of solving the following equation would probably be more convenient? $( 3 x - 15 ) ^ { 2 } = 19$

(Multiple Choice)

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Question 133

Find a power function that models the data in the table. Round to three decimal places if necessary. -The height of an object dropped from a tall building is given by the table, where t is the elapsed time in seconds and h is the height in feet. 0 1 2 3 4 5 750 734 686 606 494 350 If the height is modeled by h(t)=-16 , find .

(Multiple Choice)

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Question 134

Suppose the price p of bolts is related to the quantity q that is demanded by: $p = 620 - 4 q ^ { 2 }$ where q is measured in hundreds of bolts. Suppose the supply function for bolts is given by $p = 4 q ^ { 2 }$ where q is the number of bolts (in hundreds) that are supplied at price p. Find the equilibrium price.

(Multiple Choice)

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Question 135

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $( x + 10 ) ( x - 4 ) = - 45$

(Multiple Choice)

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Question 136

Provide an appropriate response. -If the points in the table lie on a parabola, write the equation whose graph is the parabola. -3 -2 -1 0 -1 -4 -1 8

(Multiple Choice)

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Question 137

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

(Multiple Choice)

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Question 138

Write the equation of the quadratic function whose graph is a parabola containing the given points. - $( 0,5 ) , ( - 1,5.25 ) , ( 5,18.75 )$

(Multiple Choice)

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Question 139

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } 4 x + 2 , & \text { if } x < - 2 \\x , & \text { if } - 2 \leq x \leq 3 \\3 x - 1 , & \text { if } x > 3\end{array} \right.$ $Graph the function. - f ( x ) = \left\{ \begin{array} { l l } 4 x + 2 , & \text { if } x < - 2 \\ x , & \text { if } - 2 \leq x \leq 3 \\ 3 x - 1 , & \text { if } x > 3 \end{array} \right.$

(Multiple Choice)

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Question 140

Graph the function. - $f(x)=\left\{\begin{array}{l}4 x+1, \text { if } x<0 \\3 x^{2}-2, \text { if } x \geq 0\end{array}\right.$ $Graph the function. - f(x)=\left\{\begin{array}{l} 4 x+1, \text { if } x<0 \\ 3 x^{2}-2, \text { if } x \geq 0 \end{array}\right.$

The polynomial function $\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.4 \mathrm { t }$ represents the yearly income (or loss) from a real estate investment, where t is time in years. After how many years does income begin to decline?

Use the graph of the function to estimate the x-intercepts. - $g(x)=2 x^{2}+5 x-3$ $Use the graph of the function to estimate the x-intercepts. - g(x)=2 x^{2}+5 x-3$

Use the graph of the function to estimate the x-intercepts. - $y=x^{2}-x-6$ $Use the graph of the function to estimate the x-intercepts. - y=x^{2}-x-6$

Find a quadratic function that best fits the data. Give answers to the nearest hundredth. - 2 34 79 110 1024 2345 2267 984

The profit for a product is given by $\mathrm { p } = 2204 + \mathrm { x } ^ { 2 } - 105 \mathrm { x }$ x, where x is the number of units produced and sold. Graphically find the x-intercepts of this function to find how many units will give break-even (that is return a Profit of zero).

Determine if the function is increasing or decreasing over the interval indicated. - $y = - 8 x ^ { 4 } ; x < 0$

Use the square root method to - $8 z ^ { 2 } - 1568 = 0$

Determine if the vertex of the graph is a maximum point or a minimum point. - $g ( x ) = ( x - 1 ) ^ { 2 } + 5$

$- 6 x ^ { 2 } - 7 x - 6 = 0$

Provide an appropriate response. -Which method of solving the following equation would probably be more convenient? $( 3 x - 15 ) ^ { 2 } = 19$

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $( x + 10 ) ( x - 4 ) = - 45$

Provide an appropriate response. -If the points in the table lie on a parabola, write the equation whose graph is the parabola. -3 -2 -1 0 -1 -4 -1 8

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

Write the equation of the quadratic function whose graph is a parabola containing the given points. - $( 0,5 ) , ( - 1,5.25 ) , ( 5,18.75 )$

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

Graph the function. - f(x)={4x+1, if x<03x2−2, if x≥0f(x)=\left\{\begin{array}{l}4 x+1, \text { if } x<0 \\3 x^{2}-2, \text { if } x \geq 0\end{array}\right.f(x)={4x+1, if x<03x2−2, if x≥0​

The polynomial function I(t)=−0.1t2+1.4t\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.4 \mathrm { t }I(t)=−0.1t2+1.4t represents the yearly income (or loss) from a real estate investment, where t is time in years. After how many years does income begin to decline?

Use the graph of the function to estimate the x-intercepts. - g(x)=2x2+5x−3g(x)=2 x^{2}+5 x-3g(x)=2x2+5x−3

Use the graph of the function to estimate the x-intercepts. - y=x2−x−6y=x^{2}-x-6y=x2−x−6

Find a quadratic function that best fits the data. Give answers to the nearest hundredth. - 2 34 79 110 1024 2345 2267 984

Determine if the function is increasing or decreasing over the interval indicated. - y=−8x4;x<0y = - 8 x ^ { 4 } ; x < 0y=−8x4;x<0

Use the square root method to - 8z2−1568=08 z ^ { 2 } - 1568 = 08z2−1568=0

Determine if the vertex of the graph is a maximum point or a minimum point. - g(x)=(x−1)2+5g ( x ) = ( x - 1 ) ^ { 2 } + 5g(x)=(x−1)2+5

−6x2−7x−6=0- 6 x ^ { 2 } - 7 x - 6 = 0−6x2−7x−6=0

Provide an appropriate response. -Which method of solving the following equation would probably be more convenient? (3x−15)2=19( 3 x - 15 ) ^ { 2 } = 19(3x−15)2=19

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - (x+10)(x−4)=−45( x + 10 ) ( x - 4 ) = - 45(x+10)(x−4)=−45

Provide an appropriate response. -If the points in the table lie on a parabola, write the equation whose graph is the parabola. -3 -2 -1 0 -1 -4 -1 8

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

Write the equation of the quadratic function whose graph is a parabola containing the given points. - (0,5),(−1,5.25),(5,18.75)( 0,5 ) , ( - 1,5.25 ) , ( 5,18.75 )(0,5),(−1,5.25),(5,18.75)

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

Graph the function. - $f(x)=\left\{\begin{array}{l}4 x+1, \text { if } x<0 \\3 x^{2}-2, \text { if } x \geq 0\end{array}\right.$ $Graph the function. - f(x)=\left\{\begin{array}{l} 4 x+1, \text { if } x<0 \\ 3 x^{2}-2, \text { if } x \geq 0 \end{array}\right.$

The polynomial function $\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.4 \mathrm { t }$ represents the yearly income (or loss) from a real estate investment, where t is time in years. After how many years does income begin to decline?

Use the graph of the function to estimate the x-intercepts. - $g(x)=2 x^{2}+5 x-3$ $Use the graph of the function to estimate the x-intercepts. - g(x)=2 x^{2}+5 x-3$

Use the graph of the function to estimate the x-intercepts. - $y=x^{2}-x-6$ $Use the graph of the function to estimate the x-intercepts. - y=x^{2}-x-6$

Determine if the function is increasing or decreasing over the interval indicated. - $y = - 8 x ^ { 4 } ; x < 0$

Use the square root method to - $8 z ^ { 2 } - 1568 = 0$

Determine if the vertex of the graph is a maximum point or a minimum point. - $g ( x ) = ( x - 1 ) ^ { 2 } + 5$

$- 6 x ^ { 2 } - 7 x - 6 = 0$

Provide an appropriate response. -Which method of solving the following equation would probably be more convenient? $( 3 x - 15 ) ^ { 2 } = 19$

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $( x + 10 ) ( x - 4 ) = - 45$

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

Write the equation of the quadratic function whose graph is a parabola containing the given points. - $( 0,5 ) , ( - 1,5.25 ) , ( 5,18.75 )$