### Practice Test

Use Completing the Square to solve the quadratic equation: ${a}^{2}-8a+7=23$.

Solve the following quadratic equations. Use any method.

$8{v}^{2}+3=35$

$2{b}^{2}+6b-8=0$

$\frac{4}{3}{y}^{2}-4y+3=0$

Use the discriminant to determine the number of solutions of each quadratic equation.

$3{q}^{2}-10q+12=0$

Solve by factoring, the Square Root Property, or the Quadratic Formula.

The length of a diagonal of a rectangle is three more than the width. The length of the rectangle is three times the width. Find the length of the diagonal. (Round to the nearest tenth.)

For each parabola, find ⓐ which ways it opens, ⓑ the axis of symmetry, ⓒ the vertex, ⓓ the *x*- and *y*-intercepts, and ⓔ the maximum or minimum value.

$y={x}^{2}-4$

$y=\mathrm{-3}{x}^{2}+12x-8$

Graph the following parabolas by using intercepts, the vertex, and the axis of symmetry.

$y=2{x}^{2}+6x+2$

Solve.

A water balloon is launched upward at the rate of 86 ft/sec. Using the formula $h=\mathrm{-16}{t}^{2}+86t$, find how long it will take the balloon to reach the maximum height and then find the maximum height. Round to the nearest tenth.