Write each equation in standard form. Identify the vertex, axis of symmetry, and direction of opening of the parabola.

$$y=3x^2-6x-4$$

Solve: $\frac{2 x}{x+3}-\frac{3}{x+2}=\frac{11-2 x}{x^{2}+5 x+6}$

At an open-air rock concert you are standing directly in front of a speaker. You hear the high-frequency sounds of a female vocalist as well as the low-frequency sounds of the rhythmic bass. As you walk to one side of the speaker, the sounds of the vocalist ____, and those of the rhythmic bass ____. (a) drop off noticeably; also drop off noticeably, (b) drop off only slightly; drop off noticeably, (c) drop off only slightly; also drop off only slightly, (d) drop off noticeably; drop off only slightly.

When measuring an electric field, could we use a negative rather than a positive test charge?

Use the two-way table below to answer the following question. Round the answer to the nearest whole percent. A medical researcher is investigating which of three treatments, A, B, or C, best relieves the symptoms of a chronic disease. The results are shown below.

$$\begin{matrix} & \text{Treatment A} & \text{Treatment B} & \text{Treatment C} & \text{Totals}\\ \text{Showed Improvement} & \text{293} & \text{72} & \text{203} & \text{568}\\ \text{Did Not Show Improvement} & \text{107} & \text{328} & \text{197} & \text{632}\\ \text{Totals} & \text{400} & \text{400} & \text{400} & \text{1,200}\\ \end{matrix}$$

Are the events taking treatment B and showed improvement independent? Why or why not?

Marc wants to hike from his camp to a waterfall. The waterfall is 5 miles south and 8 miles east of his campsite. Marc wants to stop for lunch halfway to the waterfall. Where should he stop?

Marc wants to hike from his camp to a waterfall. The waterfall is 5 miles south and 8 miles east of his campsite. How far away is the waterfall?

Solve each system of equations.

$$\left. \begin{array} { l } { 9 y = 8 x - 19 } \\ { 8 x + 11 = 2 y ^ { 2 } + 5 y } \end{array} \right.$$

$$x = \frac { 2 } { 3 } y ^ { 2 } - 4 y + 12$$

Find the coordinates of the center and foci and the lengths of the major and minor axes of the ellipse with the given equation. Then graph the ellipse.

$$4 y ^ { 2 } + 9 x ^ { 2 } + 16 y - 90 x + 205 = 0$$

Graph each hyperbola. Identify the vertices, foci, and asymptotes.

$$\frac { ( y + 5 ) ^ { 2 } } { 16 } - \frac { ( x + 2 ) ^ { 2 } } { 36 } = 1$$

Solve each system of equations.

$$\left. \begin{array} { l } { x ^ { 2 } + y ^ { 2 } = 100 } \\ { y = - x - 2 } \end{array} \right.$$

Find the distance between each pair of points with the given coordinates.

$$(-10, 8), (-8, -8)$$

Write an equation for an ellipse that satisfies each set of conditions. center at (-2,6), vertex at (-2,16), co-vertex at (1,6)