, ,

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 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 .

Subtract from .

Subtract from .

Remove parentheses.

Simplify .

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.

Add to both sides of the equation.

Add and .

Multiply each term in by

Multiply each term in by .

Multiply .

Multiply by .

Multiply by .

Simplify each term.

Multiply by .

Multiply by .

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 by .

Simplify by adding terms.

Add and .

Add and .

Simplify .

Simplify each term.

Apply the distributive property.

Multiply by .

Multiply by .

Simplify by adding terms.

Add and .

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 .

Add and .

Simplify .

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 (3,-12) , (-2,43) , (2,-5)