Giaro Boats manufactures a popular recreational vessel, the Revolution. To plan for expanded production and increased labor costs, the company carefully tracks current costs and income. The fixed cost to produce this boat is $\$ 108,000$ and the variable costs are $\$ 28,000$ per boat. If the Revolution sells for $\$ 40,000$, (a) find the profit function and (b) determine how many boats must be sold for the company to break even.

Binomial cubes:

$$(A+B)^3=A^3+3 A^2 B+3 A B^2+B^3$$

The cube of any binomial can be found using the formula shown, where $A$ and $B$ are the terms of the binomial. Use the formula to compute $(1-2 i)^3$ (note $A=1$ and $B=-2 i$ ).

Solve the equation using the most efficient method: factoring, square root property of equality, or the quadratic formula. Write your answer in both exact and approximate form (rounded to hundredths). Check one of the exact solutions in the original equation. $3 p^2+p=0$

Surface area of a cylinder: $A=2 \pi r h+2 \pi r^2$ If the height of a cylinder is fixed at $20 \mathrm{~cm}$, the formula becomes $A=40 \pi r+2 \pi r^2$. Write this formula in factored form and find two functions $f(r)$ and $g(r)$ such that $A(r)=(f \cdot g)(r)$. Then find $A(5)$ by direct calculation and also by computing the product of $f(5)$ and $g(5)$, then comment on the results.

Given that, $x=\frac{1}{2}+\frac{\sqrt{3}}{2} i$ and $y=\frac{1}{2}-\frac{\sqrt{3}}{2} i$ find a. $x+y$ b. $x-y$ c. $x y$

Use substitution to verify that $x=2-3 i$ is a solution to $x^2-4 x+13=0$.

Perform the operation indicated and write the result in standard form. $\frac{5 i}{1-2 i}$

Six functions are shown below, along with their respective zeroes. Use these zeroes to solve the equations.

$$\begin{gathered} f(x)=x^2+x-12 \\ f(-4)=f(3)=0 \end{gathered}$$

$$\begin{aligned} & g(x)=x^2-4 x-5 \\ & g(-1)=g(5)=0 \end{aligned}$$

$$\begin{gathered} h(x)=-2 x^2-4 x+6 \\ h(-3)=h(1)=0 \end{gathered}$$

$$\begin{gathered} j(x)=-4 x^2+4 x+8 \\ j(-1)=j(2)=0 \end{gathered}$$

$$\begin{gathered} k(x)=2 x^2+x-3 \\ k\left(\frac{-3}{2}\right)=k(1)=0 \end{gathered}$$

$$\begin{gathered} l(x)=3 x^2+8 x-3 \\ l(-3)=l\left(\frac{1}{3}\right)=0 \end{gathered}$$

$x^2+x-12=0$

Given that, $f(x)=2 x^2-x-3$ and $g(x)=x^2+5 x$, (a) determine the domain for $h(x)=f(x)-g(x)$ and (b) find $h(-2)$ using the definition.

Use a graphing calculator and the tables shown to find (a) a quadratic regression equation that models the data, (b) the output of the function for $x=3.5$, and $(c)$ the positive value of $x$ where $f(x)=39$. Round to the nearest thousandths as necessary.

$$\begin{array}{|c|c|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline 1 & -5.69 \\ \hline 3 & 0.73 \\ \hline 5 & 18.75 \\ \hline 7 & 48.37 \\ \hline 8 & 67.53 \\ \hline \end{array}$$

Graph the function using end-behavior, intercepts, and completing the square to write the function in shifted form. Clearly state the transformations used to obtain the graph, and label the vertex and all intercepts (if they exist). If the equation is not factorable, use the quadratic formula to find the $x$-intercepts. $f(x)=x^2+4 x-5$

Solve the inequality by using a graphing calculator to locate the $x$-intercepts and observing the graph. Round to the nearest hundredth as necessary. $f(x)=-5.1 x^2-3.2 x+1.9 ; f(x) \leq 0$.

(a) Apply the difference quotient to the functions given and simplify the result, then (b) find the value that the slope of the tangent line approaches when $x=2$, by investigating what happens as $h \rightarrow 0$. $d(x)=\frac{1}{2 x^2}$

Given that, $f(x)=x^2-5 x-14$, find $f(-2), f(7)$, $f(2 a)$, and $f(a-2)$.