Practice Test

529.

Use the Square Root Property to solve the quadratic equation $3 {(w + 5)}^{2} = 27 .$

530.

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

531.

Use the Quadratic Formula to solve the quadratic equation $2 m^{2} - 5 m + 3 = 0 .$

Solve the following quadratic equations. Use any method.

532.

$2 x (3 x - 2) - 1 = 0$

533.

$\frac{9}{4} y^{2} - 3 y + 1 = 0$

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

534.

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

535.

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

Solve each equation.

536.

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

537.

$y^{\frac{2}{3}} + 2 y^{\frac{1}{3}} - 3 = 0$

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.

538.

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

539.

$y = - x^{2} - 8 x - 16$

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

540.

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

541.

$f (x) = −2 x^{2} + 8 x + 4$

In the following exercises, graph each function using transformations.

542.

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

543.

$f (x) = x^{2} - 4 x - 1$

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

544.

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

545.

$2 x^{2} + x - 10 > 0$

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

546.

Find two consecutive even numbers whose product is 360.

547.

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.)

548.

A water balloon is launched upward at the rate of 86 ft/sec. Using the formula h = −16t² + 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.