Question 1

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

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 2

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?

Accepted Answer

A)  6 yr 
B)  14 yr 
C)  7 yr 
D)  9.33 yr

Question 3

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

Accepted Answer

A)  $x = - 0.5 , x = 3$ 
B)  $x = - 3 , x = 0.5$ 
C)  $x = - 2 , x = 3$ 
D)  $x = - 3 , x = - 0.5$

Question 4

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

Accepted Answer

A)  $x = - 1 , x = - 6$ 
B)  $x = - 3 , x = - 2$ 
C)  $x = - 3 , x = 2$ 
D)  $x = - 2 , x = 3$

Question 5

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.

Accepted Answer

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

Question 6

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

Accepted Answer

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)  $y = - 4.66 x ^ { 2 } - 45.67 x + 345.67$

Question 7

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).

Accepted Answer

A)  29 units 
B)  76 units 
C)  29 or 76 units 
D)  They will never break even.

Question 8

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

Accepted Answer

A)  Increasing 
B)  Decreasing

Question 9

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

Accepted Answer

A)  786 
B)  $\pm 15$ 
C)  14 
D)  $\pm 14$

Question 10

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

Accepted Answer

A)  Minimum 
B)  Maximum

Question 11

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

Accepted Answer

A)  $\frac { 7 \pm \sqrt { 95 } } { - 12 }$ 
B)  $\frac { - 7 \pm \sqrt { 95 } } { - 12 }$ 
C)  $\frac { - 7 \pm i \sqrt { 95 } } { - 12 }$ 
D)  $\frac { 7 \pm i \sqrt { 95 } } { - 12 }$

Question 12

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 $\mathrm { v } _ { 0 }$.

Accepted Answer

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

Question 13

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

Accepted Answer

A)  Completing the square 
B)  Square root property

Question 14

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. $$\begin{array}{l}
\begin{array} { r | r r r r r r } 
\mathrm { t } & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \mathrm { h } & 750 & 734 & 686 & 606 & 494 & 350
\end{array}\
\text { If the height is modeled by } h ( t ) = h _ { 0 } - 16 t ^ { 2 } \text {, find } h _ { 0 } \text {. }
\end{array}$$

Accepted Answer

A)  375 ft 
B)  750 ft 
C)  1125 ft 
D)  1500 ft

Question 15

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.

Accepted Answer

A)  $620 
B)  $310 
C)  $9 
D)  $325

Question 16

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

Accepted Answer

A)  $- 41 , - 10$ 
B)  $- 10,4$ 
C)  $4 , - 55$ 
D)  $- 1 , - 5$

Question 17

Provide an appropriate response.
-If the points in the table lie on a parabola, write the equation whose graph is the parabola. $\begin{array}{c|c|c|c|c}
\mathrm{x} & -3 & -2 & -1 & 0 \
\hline \mathrm{y} & -1 & -4 & -1 & 8
\end{array}$

Accepted Answer

A)  $y = 3 x ^ { 2 } + 12 x + 8$ 
B)  $y = 3 x ^ { 2 } + 12 x - 8$ 
C)  $y = 3 ( x + 2 ) ^ { 2 } + 4$ 
D)  $y = 3 ( x - 2 ) ^ { 2 } + 4$

Question 18

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

Accepted Answer

A)  Concave down 
B)  Concave up

Question 19

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

Accepted Answer

A)  $y = \frac { x ^ { 2 } } { 2 } + \frac { x } { 4 } - 5$ 
B)  $y = \frac { x ^ { 2 } } { 2 } + 2 x + 5$ 
C)  $y = \frac { x ^ { 2 } } { 2 } + \frac { x } { 4 } + 5$ 
D)  $y = \frac { x ^ { 2 } } { 4 } + \frac { x } { 2 }$

Question 20

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

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

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

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

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. - $g(x) =2 x^{2}+5 x-3$ $Use the graph of the function to estimate the x-intercepts. - g(x) =2 x^{2}+5 x-3 A) x = - 0.5 , x = 3 B) x = - 3 , x = 0.5 C) x = - 2 , x = 3 D) x = - 3 , x = - 0.5$

Use the graph of the function to estimate the x-intercepts. - $y=x^{2}-x-6$ $Use the graph of the function to estimate the x-intercepts. - y=x^{2}-x-6 A) x = - 1 , x = - 6 B) x = - 3 , x = - 2 C) x = - 3 , x = 2 D) x = - 2 , x = 3$

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

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. $\begin{array}{c|c|c|c|c}\mathrm{x} & -3 & -2 & -1 & 0 \\\hline \mathrm{y} & -1 & -4 & -1 & 8\end{array}$

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. - $( 0,5 ) , ( - 1,5.25 ) , ( 5,18.75 )$

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. - x23479110y102423452267984\begin{array}{c|c|c|c|c}\mathrm{x} & 2 & 34 & 79 & 110 \\\hline \mathrm{y} & 1024 & 2345 & 2267 & 984\end{array}xy​21024​342345​792267​110984​​

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

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)

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

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. - $g(x) =2 x^{2}+5 x-3$ $Use the graph of the function to estimate the x-intercepts. - g(x) =2 x^{2}+5 x-3 A) x = - 0.5 , x = 3 B) x = - 3 , x = 0.5 C) x = - 2 , x = 3 D) x = - 3 , x = - 0.5$

Use the graph of the function to estimate the x-intercepts. - $y=x^{2}-x-6$ $Use the graph of the function to estimate the x-intercepts. - y=x^{2}-x-6 A) x = - 1 , x = - 6 B) x = - 3 , x = - 2 C) x = - 3 , x = 2 D) x = - 2 , x = 3$

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

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. - $( 0,5 ) , ( - 1,5.25 ) , ( 5,18.75 )$