Examples

Find the Parabola Through (1,1) with Vertex (0,0)
,
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
Using to solve for , .
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Step 2.1
Rewrite the equation as .
Step 2.2
Simplify .
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Step 2.2.1
Add and .
Step 2.2.2
Subtract from .
Step 2.2.3
One to any power is one.
Step 2.2.4
Multiply by .
Step 3
Using , the general equation of the parabola with the vertex and is .
Step 4
Solve for .
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Step 4.1
Remove parentheses.
Step 4.2
Multiply by .
Step 4.3
Remove parentheses.
Step 4.4
Simplify .
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Step 4.4.1
Add and .
Step 4.4.2
Multiply by .
Step 4.4.3
Subtract from .
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
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