Algebra Examples

Find the Parabola Through (-1,-5) with Vertex (2,3)
,
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 , .
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Rewrite the equation as .
Simplify each term.
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Multiply by .
Subtract from .
Raise to the power of .
Move to the left of the expression .
Multiply by .
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Subtract from .
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 .
Using , the general equation of the parabola with the vertex and is .
Solve for .
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Remove the extra parentheses.
Remove the parentheses around the expression .
Simplify each term.
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Multiply by .
Rewrite as .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Remove parentheses.
Simplify and combine like terms.
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Simplify each term.
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Use the power rule to combine exponents.
Add and .
Move to the left of the expression .
Multiply by .
Multiply by .
Subtract from .
Apply the distributive property.
Simplify.
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Simplify .
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Write as a fraction with denominator .
Multiply and .
Simplify .
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Multiply by .
Write as a fraction with denominator .
Multiply and .
Multiply by .
Write as a fraction with denominator .
Multiply and .
Simplify .
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Multiply by .
Write as a fraction with denominator .
Multiply and .
Multiply by .
Simplify each term.
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Move to the left of the expression .
Multiply by .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Multiply by .
Add and .
Move the negative in front of the fraction.
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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