# Algebra Examples

,

Step 1

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 .

Step 2

Step 2.1

Rewrite the equation as .

Step 2.2

Simplify .

Step 2.2.1

Add and .

Step 2.2.2

Subtract from .

Step 2.2.3

Raise to the power of .

Step 2.2.4

Move to the left of .

Step 2.3

Divide each term in by and simplify.

Step 2.3.1

Divide each term in by .

Step 2.3.2

Simplify the left side.

Step 2.3.2.1

Cancel the common factor of .

Step 2.3.2.1.1

Cancel the common factor.

Step 2.3.2.1.2

Divide by .

Step 2.3.3

Simplify the right side.

Step 2.3.3.1

Cancel the common factor of and .

Step 2.3.3.1.1

Factor out of .

Step 2.3.3.1.2

Cancel the common factors.

Step 2.3.3.1.2.1

Factor out of .

Step 2.3.3.1.2.2

Cancel the common factor.

Step 2.3.3.1.2.3

Rewrite the expression.

Step 3

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

Step 4

Step 4.1

Remove parentheses.

Step 4.2

Multiply by .

Step 4.3

Remove parentheses.

Step 4.4

Simplify .

Step 4.4.1

Simplify by adding zeros.

Step 4.4.1.1

Add and .

Step 4.4.1.2

Subtract from .

Step 4.4.2

Combine and .

Step 5

The standard form and vertex form are as follows.

Standard Form:

Vertex Form:

Step 6

Simplify the standard form.

Standard Form:

Vertex Form:

Step 7