# Find the Parabola Through (2,6) with Vertex (1,3) (1,3) , (2,6) ,
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 each term.
Multiply by .
Subtract from .
One to any power is one.
Multiply by .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
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 .
Rewrite as .
Rewrite as .
Multiply by .
Subtract from .
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
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 (2,6) with Vertex (1,3) (1,3) , (2,6)     