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

Find the requested value. - $f ( - 6 )$ for $f ( x ) = \left\{ \begin{array} { c } 6 x , \text { if } x \leq - 1 \\ x - 2 , \text { if } x > - 1 \end{array} \right.$

Determine if the vertex of the graph is a maximum point or a minimum point. - $y = - \frac { 2 } { 5 } ( x + 3 ) ^ { 2 } - 1$

Use the square root method to - $y ^ { 2 } = 5$

A study in a small town showed that the percent of residents who have college degrees can be modeled by the function $\mathrm { P } = 37 \mathrm { x } ^ { 0.33 }$ where x is the number of years since 2005. Does this model indicate that the percent of Residents with a college degree is increasing or decreasing?

When water runs out of a hole in a cylindrical container, the height of the water in the container can often be modeled by a quadratic function. Assume that the height of the water in a particular metal can with a small hole can be modeled by $h = 0.0005 x ^ { 2 } - 0.17 x + 8$ , where x is the time (sec) and h is the height (cm). Use the quadratic formula to estimate The time when the height is 5 cm. Round your answer to the nearest second.

Determine if the graph of the function is concave up or concave down - $f ( x ) = 2 x ^ { 2 } + 2 x - 4$

Solve the equation by completing the square. - $\mathrm { p } ^ { 2 } + 3 \mathrm { p } - 9 = 0$

Use the quadratic formula to - $8 y ^ { 2 } + 30 y + 25 = 0$

Find a power function that models the data in the table. Round to three decimal places if necessary. - 1 2 3 4 5 6 7 8 9 1.2 26.6 172.0 645.2 1801.9 4165.5 8291.1 15,600.0 28,953.4

Given the following revenue and cost functions, find the maximum profit. (Recall that profit equals revenue minus cost.) $R ( x ) = 80 x - 2 x ^ { 2 } ; C ( x ) = 24 x + 100$

Use the square root method to - $2 x ^ { 2 } = 30$

The present value that will give a future value S in 4 years with interest compounded annually varies inversely as the fourth power of $1 + r$ r, where r is the annual interest rate. If the present value of $3.71 gives a future value Of $5000, what would be the present value of $10,000? Round to the nearest dollar.

Given the following revenue and cost functions, find the x-value that makes revenue a maximum. $R ( x ) = 84 x - 2 x ^ { 2 } ; C ( x ) = 22 x + 101$

Graph - $f(x)=(x-1)^{1 / 3}$

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $3 x ^ { 2 } + 5 x - 7 = 0$

Use the square root method to - $x ^ { 2 } - 64 = 0$

Explain in your own words a sequence of steps that can be used to solve any quadratic equation in the most efficient way.

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $x ^ { 2 } - 6 x - 57 = 0$

Graph - $f(x)=\frac{1}{x+2}$

Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. - $5 x ^ { 2 } - 45 x + 100 = 0$