, ,

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.

Simplify each equation.

Remove parentheses.

Simplify .

Simplify each term.

Raising to any positive power yields .

Multiply by .

Multiply by .

Combine the opposite terms in .

Add and .

Add and .

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 .

Rewrite the equation as .

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Replace all occurrences of in with .

Simplify.

Remove parentheses.

Remove parentheses.

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 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.

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.

Divide by .

Replace all occurrences of in with .

Simplify .

Simplify each term.

Apply the distributive property.

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 .

Multiply by .

Simplify by adding terms.

Add and .

Add and .

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.

Add and .

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 in with .

Simplify .

Simplify each term.

Divide 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 (0,1) , (2,-3) , (4,-7)