Precalculus Examples

Find the Parabola Through (-6,6) with Vertex (0,0)
,
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 .
Using to solve for , .
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Rewrite the equation as .
Simplify the left side.
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Simplify each term.
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Subtract from to get .
Raise to the power of to get .
Move to the left of the expression .
Multiply by to get .
Add and to get .
Divide each term by and simplify.
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Divide each term in by .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by to get .
Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Using , the general equation of the parabola with the vertex and is .
Solve for to get .
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Remove the extra parentheses.
Remove the parentheses around the expression .
Simplify each term.
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Subtract from to get .
Remove parentheses around .
Simplify .
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Write as a fraction with denominator .
Multiply and 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:
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