# 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 to get .

Rewrite the equation as .

Simplify each term.

Multiply by to get .

Subtract from to get .

Remove parentheses around .

Raise to the power of to get .

Move to the left of the expression .

Multiply by to get .

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

Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.

Add and to get .

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 to get .

Divide by to get .

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 to get .

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 to get .

Move to the left of the expression .

Multiply by to get .

Rewrite as .

Rewrite as .

Multiply by to get .

Subtract from to get .

Apply the distributive property.

Simplify.

Multiply by to get .

Multiply by to get .

Simplify by subtracting numbers.

Subtract from to get .

Add and to get .

The standard form and vertex form are as follows.

Standard Form:

Vertex Form:

Simplify the standard form.

Standard Form:

Vertex Form: