# Radicals and quadratics

Please see attachment.

Write the following expression in simplified radical form.

Find the roots of the quadratic equation:

Compute the value of the discriminant and give the number of real solutions to the quadratic equation

Solve the following equation for by using the quadratic formula:

Find the -intercept(s) and the coordinates of the vertex for the parabola . If there is more than one -intercept, separate them with commas.

#### Solution Preview

Hi,

Please find the solutions/explanations attached herewith.

1. Rewrite the following in simplified radical form.

Assume that all variables represent positive real numbers

Solution:

2. Write the following expression in simplified radical form.

Assume that all variables represent positive real numbers.

Solution:

3. Simplify the following expression as much as possible:

Assume that all variables represent positive real numbers.

Solution:

4.

Simplify.

Assume that all variables represent positive real numbers.

Solution:

5.

Multiply. Simplify your answer as much as possible.

Solution:

By combining similar terms, we will get

6.

Rationalize the denominator and simplify:

Solution:

7.

Write in simplified radical form by rationalizing the denominator.

Solution:

8.

Solve for :

,

where is a real number.

(If there is more than one solution, separate them with commas.)

Solution:

Squaring each side, we will get

z + 13 = 9

Subtract 13 from each side, we will get

z = 9 - 13 = -4

9.

Solve the following equation for :

,

where is a real number.

(If there is more than one solution, ...

#### Solution Summary

This provides several examples of working with radicals and quadratic equations, including graphing parabolas, simplifying, solving equations, and word problems.