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
Multiply by .
Step 2.2.2
Subtract from .
Step 2.2.3
Raise to the power of .
Step 2.2.4
Move to the left of .
Step 2.3
Move all terms not containing to the right side of the equation.
Step 2.3.1
Add to both sides of the equation.
Step 2.3.2
Add and .
Step 2.4
Divide each term in by and simplify.
Step 2.4.1
Divide each term in by .
Step 2.4.2
Simplify the left side.
Step 2.4.2.1
Cancel the common factor of .
Step 2.4.2.1.1
Cancel the common factor.
Step 2.4.2.1.2
Divide by .
Step 2.4.3
Simplify the right side.
Step 2.4.3.1
Divide by .
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 .
Step 4.4.1
Simplify each term.
Step 4.4.1.1
Multiply by .
Step 4.4.1.2
Rewrite as .
Step 4.4.1.3
Expand using the FOIL Method.
Step 4.4.1.3.1
Apply the distributive property.
Step 4.4.1.3.2
Apply the distributive property.
Step 4.4.1.3.3
Apply the distributive property.
Step 4.4.1.4
Simplify and combine like terms.
Step 4.4.1.4.1
Simplify each term.
Step 4.4.1.4.1.1
Multiply by .
Step 4.4.1.4.1.2
Move to the left of .
Step 4.4.1.4.1.3
Rewrite as .
Step 4.4.1.4.1.4
Rewrite as .
Step 4.4.1.4.1.5
Multiply by .
Step 4.4.1.4.2
Subtract from .
Step 4.4.1.5
Apply the distributive property.
Step 4.4.1.6
Simplify.
Step 4.4.1.6.1
Multiply by .
Step 4.4.1.6.2
Multiply by .
Step 4.4.2
Combine the opposite terms in .
Step 4.4.2.1
Subtract from .
Step 4.4.2.2
Add and .
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