# 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

Cancel the common factor of and .

Step 1.1.3.2.1.1

Factor out of .

Step 1.1.3.2.1.2

Cancel the common factors.

Step 1.1.3.2.1.2.1

Factor out of .

Step 1.1.3.2.1.2.2

Cancel the common factor.

Step 1.1.3.2.1.2.3

Rewrite the expression.

Step 1.1.3.2.2

Cancel the common factor of and .

Step 1.1.3.2.2.1

Factor out of .

Step 1.1.3.2.2.2

Cancel the common factors.

Step 1.1.3.2.2.2.1

Factor out of .

Step 1.1.3.2.2.2.2

Cancel the common factor.

Step 1.1.3.2.2.2.3

Rewrite the expression.

Step 1.1.3.2.2.2.4

Divide by .

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

Raising to any positive power yields .

Step 1.1.4.2.1.2

Multiply by .

Step 1.1.4.2.1.3

Divide by .

Step 1.1.4.2.1.4

Multiply by .

Step 1.1.4.2.2

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