### Practice Test

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

Solve the following quadratic equations. Use any method.

$2x\left(3x-2\right)-1=0$

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

$6{p}^{2}-13p+7=0$

Solve each equation.

$4{x}^{4}-17{x}^{2}+4=0$

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

$y=3{x}^{2}+6x+8$

Graph each quadratic function using intercepts, the vertex, and the equation of the axis of symmetry.

$f\left(x\right)={x}^{2}+6x+9$

In the following exercises, graph each function using transformations.

$f(x)={\left(x+3\right)}^{2}+2$

In the following exercises, solve each inequality algebraically and write any solution in interval notation.

${x}^{2}-6x-8\le 0$

Model the situation with a quadratic equation and solve by any method.

Find two consecutive even numbers whose product is 360.

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.)

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