Use a graphing utility to graph each pair of equations on the same set of axes. Determine how the two equations are related.

$y_1=x^3-3 x^2$ and $y_2=x^3+3 x^2-4$

Engineers are designing a stretch of highway in a valley. They want to install a storm drain at its lowest point. The equation for the transition curve is $y=0.00004 x^2-0.05 x+1100$. Determine the coordinates of the storm drain, to the nearest unit.

Express the equation of the given line in standard form. Then find the distance from the given point $P\left(x_1, y_1\right)$ to that line. Round answers to the nearest hundredth.

The line is perpendicular to the line $2 y=3 x-4$ and passes through the origin; $P(2,-5)$.

How would you determine the cubic polynomial that has the solutions $-3,-2$, and $7$ ?

Solve each polynomial equation.

$$x^3-4 x^2+4 x-16=0$$

A ball thrown in space where there is virtually zero gravity would travel in a straight line at a constant speed. The data below was collected.

$$\begin{array}{c|c} \text{Time (s)} & \text{Distance (ft)} \\ \hline 10 & 5.70 \\ 0.2& 8.5 \\ 0.5& 16.6 \\ 0.7& 22.0 \\ 1.5& 43.6 \end{array}$$

Find an equation giving the distance traveled as a function of time.

Solve each polynomial equation. If a solution occurs more than once, state its multiplicity.

$$x^3+x^2-9 x-9=0$$

Express each quadratic function in the form $f(x)=a(x-h)^2+k$. Then use transformations of the graph of $f(x)=x^2$ to graph each function.

$$f(x)=-2 x^2-5$$

Solve.

$$-\frac{42}{y}=\frac{y-25}{3}$$

Determine the symmetries of each equation. Then use the properties of symmetry to graph each equation.

$$x y^2-1$$

Show that $P(1,1), Q(5,4), R(9,1)$, and $S(5,-2)$ are the vertices of a rhombus.

Express the equation of the given line in the form $A x+B y+C=0$. Then find the distance from the given point $P\left(x_1, y_1\right)$ to that line. Round answers to the nearest hundredth.

$$x=3 ; P(5,7)$$

Solve each quadratic equation by an appropriate method.

$$x^2-10 x+70=0$$

Determine the equation of the line satisfying the given conditions:

Passes through the point $(-2,-4)$ and has slope of $-2$