# Find the Equation of the Parabola (1,7) , (2,2) , (4,-32)

, ,
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.
One to any power is one.
Multiply by .
Multiply by .
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.
Simplify .
Simplify each term.
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Multiply by .
Simplify .
Simplify each term.
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Multiply by .
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.
Add to 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 each term.
Divide by .
Move the negative in front of the fraction.
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Replace all occurrences of in with .
Simplify each equation.
Simplify .
Simplify each term.
Apply the distributive property.
Multiply by .
Multiply .
Multiply by .
Multiply by .
Subtract from .
To write as a fraction with a common denominator, multiply by .
Simplify terms.
Combine and .
Combine the numerators over the common denominator.
Simplify each term.
Simplify the numerator.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Multiply by .
Subtract from .
Multiply by .
Simplify .
Simplify each term.
Apply the distributive property.
Multiply by .
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Subtract from .
Subtract from .
Solve for in the third equation.
Rewrite the equation as .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
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 .
Divide by .
Simplify .
Simplify each term.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Multiply by .
Subtract from .
Substitute the actual values of ,, and into the formula for a quadratic equation to find the resulting equation.
Find the Equation of the Parabola (1,7) , (2,2) , (4,-32)