# Algebra Examples

Step 1

Write as an equation.

Step 2

Since is on the right side of the equation, switch the sides so it is on the left side of the equation.

Step 3

Subtract from both sides of the equation.

Step 4

Step 4.1

Reorder and .

Step 4.2

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

Step 4.3

Consider the vertex form of a parabola.

Step 4.4

Find the value of using the formula .

Step 4.4.1

Substitute the values of and into the formula .

Step 4.4.2

Simplify the right side.

Step 4.4.2.1

Multiply by .

Step 4.4.2.2

Move the negative in front of the fraction.

Step 4.5

Find the value of using the formula .

Step 4.5.1

Substitute the values of , and into the formula .

Step 4.5.2

Simplify the right side.

Step 4.5.2.1

Simplify each term.

Step 4.5.2.1.1

Raise to the power of .

Step 4.5.2.1.2

Multiply by .

Step 4.5.2.2

Subtract from .

Step 4.6

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

Step 5

Step 5.1

Add to both sides of the equation.

Step 5.2

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

Step 5.3

Combine and .

Step 5.4

Combine the numerators over the common denominator.

Step 5.5

Simplify the numerator.

Step 5.5.1

Multiply by .

Step 5.5.2

Add and .

Step 5.6

Move the negative in front of the fraction.

Step 6

Step 6.1

Divide each term in by .

Step 6.2

Simplify the left side.

Step 6.2.1

Cancel the common factor of .

Step 6.2.1.1

Cancel the common factor.

Step 6.2.1.2

Divide by .

Step 6.3

Simplify the right side.

Step 6.3.1

Simplify each term.

Step 6.3.1.1

Multiply the numerator by the reciprocal of the denominator.

Step 6.3.1.2

Multiply .

Step 6.3.1.2.1

Multiply by .

Step 6.3.1.2.2

Multiply by .

Step 7

Step 7.1

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

Step 7.2

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Step 7.2.1

Multiply by .

Step 7.2.2

Multiply by .

Step 7.3

Combine the numerators over the common denominator.

Step 7.4

Move to the left of .

Step 7.5

Reorder terms.