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

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $25 y ^ { 2 } + 20 y + 4 = 0$

Graph - $y=x^{3}-3$

Graph - $y = \frac { 3 } { x }$

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

Determine whether a linear or quadratic function would be a more appropriate model for the graphed data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the coefficient of $x ^ { 2 }$ should be positive or negative. $\text {CRIME STATISTICS}$ $\text {Years since 2000}$

Find a power function that models the data in the table. Round to three decimal places if necessary. - 1 2 3 4 5 4 14 39 60 120

Use the graph of the function to estimate the x-intercepts. - $f(x)=-x^{2}+4 x+5$

Given the following revenue and cost functions, find the x-value that makes profit a maximum. (Recall that profit equals revenue minus cost.) $R ( x ) = 58 x - 2 x ^ { 2 } ; C ( x ) = 25 x + 98$

Graph the function. - $f(x)=\left\{\begin{array}{ll}-1, & \text { if } x \geq 1 \\-5-x, & \text { if } x<1\end{array}\right.$

Solve the equation. - $| x | = x ^ { 2 } + 7 x$

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } x + 5 , & \text { if } x > 0 \\1 , & \text { if } x \leq 0\end{array} \right.$

Find the requested value. - $f ( - 5 )$ for $f ( x ) = \left\{ \begin{array} { c l } 6 x + 1 & \text { if } x < 5 \\ 5 x & \text { if } 5 \leq x \leq 8 \\ 5 - 6 x & \text { if } x > 8 \end{array} \right.$

Graph the quadratic equation on [ $[ - 10,10 ] \text { by } [ - 10,10 ]$ oes this window give a complete graph? - $f(x)=4 x^{2}-2 x+2$

The number of mice in an old barn after the cats are removed can be roughly estimated with the following function: $y = 2.325 x ^ { 0.73 } + 0.26 x + 1$ where y is the number of mice and x is the number of weeks since a cat lived In the barn. Predict the number of mice there will be in ten weeks if you get rid of the cat in the barn.

Determine if the vertex of the graph is a maximum point or a minimum point. - $f ( x ) = 3 x ^ { 2 } + 2 x + 2$

The average number of prisoners in a county jail is modeled by y $y = 0.15 x ^ { 2 } + 10.34 x + 114.16$ , where x is the number of years after 2000. 1. Graph this function from 0 to 30. 2. Approximate, to the nearest whole number, how many prisoners there will be in 2010. 3. Does this model indicate that the number of prisoners will increase or decrease from 2000 to 2030?

A salesperson gets a commission of $800 for the first $10,000 of sales, and then $400 for each additional $10,000 or partial of sales. Let S(x) represent the commission on x dollars of sales. Find the value of S(95,000).

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

You are given a graph of a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ for different values of $a , b$ , and $c$ . For this function, a. Determine whether the discriminant is positive, negative, or zero. b. Determine if there are 0,1 , or 2 real solutions to $f ( x ) = 0$ . c. Solve the equation $f ( x ) = 0$ . -A grasshopper is perched on a reed 5 inches above the ground. It hops off the reed and lands on the ground about 7.9 inches away. During its hop, its height is given by the equation $h = - 0.3 x ^ { 2 } + 1.75 x + 5$ , where x is the Distance in inches from the base of the reed, and h is in inches. How far was the grasshopper from the base of The reed when it was 3.25 inches above the ground? Round to the nearest tenth.