Find the Parabola Through (0,-12) with Vertex (-2,-20) (-2,-20) , (0,-12)

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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 .
Using to solve for , .
Rewrite the equation as .
Simplify .
Subtract from .
Simplify each term.
Multiply by .
Raise to the power of .
Move to the left of .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Using , the general equation of the parabola with the vertex and is .
Solve for .
Remove parentheses.
Simplify .
Simplify each term.
Multiply by .
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Move to the left of .
Multiply by .
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Subtract from .
The standard form and vertex form are as follows.
Standard Form:
Vertex Form:
Simplify the standard form.
Standard Form:
Vertex Form:
Find the Parabola Through (0,-12) with Vertex (-2,-20) (-2,-20) , (0,-12)

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