# Find the Equation of the Parabola (3,1) , (-3,-5) , (9,-5)

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Use the standard form of a quadratic equation as the starting point for finding the equation through the three points.
Create a system of equations by substituting the and values of each point into the standard formula of a quadratic equation to create the three equation system.
Solve the system of equations to find the values of , , and .
Simplify each equation.
Remove parentheses.
Simplify each term.
Raise to the power of .
Move to the left of .
Move to the left of .
Remove parentheses.
Simplify each term.
Raise to the power of .
Move to the left of .
Move to the left of .
Remove parentheses.
Simplify each term.
Raise to the power of .
Move to the left of .
Move to the left of .
Solve for in the first equation.
Rewrite the equation as .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from both sides of the equation.
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Replace all occurrences of in with .
Simplify each equation.
Remove parentheses.
Simplify .
Combine the opposite terms in .
Subtract from .
Subtract from .
Remove parentheses.
Simplify .
Subtract from .
Subtract from .
Solve for in the second equation.
Rewrite the equation as .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Replace all occurrences of in with .
Simplify.
Simplify .
Multiply by .
Subtract from .
Simplify .
Multiply by .
Solve for in the third equation.
Rewrite the equation as .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Replace all occurrences of in with .
Simplify .
Simplify each term.
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Multiply by .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
Substitute the actual values of ,, and into the formula for a quadratic equation to find the resulting equation.
Find the Equation of the Parabola (3,1) , (-3,-5) , (9,-5)