Exam 2: Linear and Quadratic Functions

Graph the function using its vertex, axis of symmetry, and intercepts. - $f ( x ) = - 3 x ^ { 2 } - 2 x - 10$ A) vertex $\left( - \frac { 1 } { 3 } , - \frac { 29 } { 3 } \right)$ intercept $( 0 , - 10 )$ B) vertex $\left( \frac { 1 } { 3 } , - \frac { 29 } { 3 } \right)$ intercept $( 0 , - 10 )$ C) vertex $\left( \frac { 1 } { 3 } , \frac { 29 } { 3 } \right)$ intercept $( 0,10 )$ D) vertex $\left( - \frac { 1 } { 3 } , \frac { 29 } { 3 } \right)$ intercept $( 0,10 )$

Solve the problem. -A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of $192 \mathrm { ft } / \mathrm { sec }$ , and the gorge is $560 \mathrm { ft }$ deep, during what interval can the flare be seen? $\left( h = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 } \right. \text { ) }$

Solve the problem. -Marty's Tee Shirt & Jacket Company is to produce a new line of jackets with an embroidery of a Great Pyrenees dog on the front. There are fixed costs of $560 to set up for production, and variable costs of $33 per jacket. Write An equation that can be used to determine the total cost, C(x), encountered by Marty's Company in producing x Jackets.

Use factoring to find the zeros of the quadratic function. List the x-intercepts of the graph of the function. - $h ( x ) = 4 x ^ { 2 } - 8 x$

Use a graphing calculator to plot the data and find the quadratic function of best fit. -The number of housing starts in one beachside community remained fairly level until 1992 and then began to increase. The following data shows the number of housing starts since 1992 (x = 1). Use a graphing calculator to Plot a scatter diagram. What is the quadratic function of best fit? Year, x Housing Starts, H 1 200 2 205 3 210 4 240 5 245 6 230 7 220 8 210

Solve the problem. -Marty's Tee Shirt & Jacket Company is to produce a new line of jackets with a embroidery of a Great Pyrenees dog on the front. There are fixed costs of $650 to set up for production, and variable costs of $39 per jacket. Write An equation that can be used to determine the total cost, C(x), encountered by Marty's Company in producing x Jackets, and use the equation to find the total cost of producing 79 jackets.

Determine the average rate of change for the function. - $f ( x ) = \frac { 1 } { 2 } x - 3$

Find the real zeros, if any, of each quadratic function using the quadratic formula. List the x-intercepts, if any, of the graph of the function. - $g ( x ) = x ^ { 2 } - 12 - 5 x$

Determine if the type of relation is linear, nonlinear, or none. -

Use the slope and y-intercept to graph the linear function. - $\mathrm { F } ( \mathrm { x } ) = \frac { 1 } { 6 } \mathrm { x }$ A) B) C) D)

Determine the slope and y-intercept of the function. - $F ( x ) = - \frac { 1 } { 4 } x$

Graph the function using its vertex, axis of symmetry, and intercepts. - $f(x)=-x^{2}-2 x+8$ A) vertex $( - 1,9 )$ intercepts $( 2,0 ) , ( - 4,0 ) , ( 0,8 )$ B) vertex $( 1 , - 9 )$ intercepts $( - 2,0 ) , ( 4,0 ) , ( 0 , - 8 )$ C) vertex $( - 1 , - 9 )$ intercepts $( 2,0 ) , ( - 4,0 ) , ( 0 , - 8 )$ D) vertex $( 1,9 )$ intercepts $( - 2,0 ) , ( 4,0 ) , ( 0,8 )$

Solve the problem. -To convert a temperature from degrees Celsius to degrees Fahrenheit, you multiply the temperature in degrees Celsius by 1.8 and then add 32 to the result. Express F as a linear function of c. A) $F ( c ) = 1.8 + 32 c$ B) $F ( c ) = 1.8 c + 32$ C) $\mathrm { F } ( \mathrm { c } ) = \frac { \mathrm { c } - 32 } { 1.8 }$ D) $F ( c ) = 33.8 \mathrm { c }$

Solve the problem. -The following data represents the amount of money Tom is saving each month since he graduated from college. month 1 2 3 4 5 6 7 savings \ 52 \ 70 \ 81 \ 91 \ 102 \ 118 \ 132 Using the line of best fit for the data set, predict the amount he will save in the 24th month after graduating from college.

Solve the problem. -The manufacturer of a CD player has found that the revenue R (in dollars) is $R ( p ) = - 4 p ^ { 2 } + 1,910 p$ when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar?

Solve the problem. -The price p (in dollars) and the quantity x sold of a certain product obey the demand equation $x = - 6 p + 120 , \quad 0 \leq p \leq 20$ What quantity x maximizes revenue? What is the maximum revenue?

Solve the inequality. Express your answer using interval notation. Graph the solution set. - $| 6 x | < 24$

Find the zeros of the quadratic function by completing the square. List the x-intercepts of the graph of the function. - $f ( x ) = 16 x ^ { 2 } + 56 x + 13$

Solve the problem. -If $g ( x ) = 70 x ^ { 2 } - 70$ and $h ( x ) = 51 x$ , then solve $g ( x ) > h ( x )$ .

Use factoring to find the zeros of the quadratic function. List the x-intercepts of the graph of the function. - $G ( x ) = x ^ { 2 } - 5 x$