# Algebra Examples

Step 1

Step 1.1

Complete the square for .

Step 1.1.1

Use the form , to find the values of , , and .

Step 1.1.2

Consider the vertex form of a parabola.

Step 1.1.3

Find the value of using the formula .

Step 1.1.3.1

Substitute the values of and into the formula .

Step 1.1.3.2

Simplify the right side.

Step 1.1.3.2.1

Multiply by .

Step 1.1.3.2.2

Move the negative in front of the fraction.

Step 1.1.4

Find the value of using the formula .

Step 1.1.4.1

Substitute the values of , and into the formula .

Step 1.1.4.2

Simplify the right side.

Step 1.1.4.2.1

Simplify each term.

Step 1.1.4.2.1.1

Raise to the power of .

Step 1.1.4.2.1.2

Multiply by .

Step 1.1.4.2.1.3

Move the negative in front of the fraction.

Step 1.1.4.2.1.4

Multiply .

Step 1.1.4.2.1.4.1

Multiply by .

Step 1.1.4.2.1.4.2

Multiply by .

Step 1.1.4.2.2

To write as a fraction with a common denominator, multiply by .

Step 1.1.4.2.3

Combine and .

Step 1.1.4.2.4

Combine the numerators over the common denominator.

Step 1.1.4.2.5

Simplify the numerator.

Step 1.1.4.2.5.1

Multiply by .

Step 1.1.4.2.5.2

Add and .

Step 1.1.5

Substitute the values of , , and into the vertex form .

Step 1.2

Set equal to the new right side.

Step 2

Use the vertex form, , to determine the values of , , and .

Step 3

Find the vertex .

Step 4