# Algebra Examples

,

The general equation of a parabola with vertex is . In this case we have as the vertex and is a point on the parabola. To find , substitute the two points in .

Rewrite the equation as .

Simplify each term.

Multiply by .

Subtract from .

Raise to the power of .

Move to the left of the expression .

Multiply by .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by .

Using , the general equation of the parabola with the vertex and is .

Remove the extra parentheses.

Remove the parentheses around the expression .

Simplify each term.

Multiply by .

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Remove parentheses.

Simplify and combine like terms.

Simplify each term.

Use the power rule to combine exponents.

Add and .

Move to the left of the expression .

Multiply by .

Multiply by .

Subtract from .

Apply the distributive property.

Simplify.

Simplify .

Write as a fraction with denominator .

Multiply and .

Simplify .

Multiply by .

Write as a fraction with denominator .

Multiply and .

Multiply by .

Write as a fraction with denominator .

Multiply and .

Simplify .

Multiply by .

Write as a fraction with denominator .

Multiply and .

Multiply by .

Simplify each term.

Move to the left of the expression .

Multiply by .

Move the negative in front of the fraction.

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

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

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Multiply by .

Add and .

Move the negative in front of the fraction.

The standard form and vertex form are as follows.

Standard Form:

Vertex Form:

Simplify the standard form.

Standard Form:

Vertex Form: