# Precalculus 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 each term.

Step 2.2.1

Subtract from .

Step 2.2.2

One to any power is one.

Step 2.2.3

Multiply by .

Step 2.3

Subtract from both sides of the equation.

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 each term.

Step 4.4.1

Subtract from .

Step 4.4.2

Rewrite as .

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