# Precalculus Examples

, ,

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.

One to any power is one.

Multiply by .

Multiply by .

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 third equation.

Rewrite the equation as .

Move all terms not containing to the right side of the equation.

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 .

Replace all occurrences of in with .

Simplify .

Simplify each term.

Apply the distributive property.

Multiply by .

Multiply by .

Simplify by adding terms.

Add and .

Add and .

Solve for in the second 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 .

Multiply by .

Subtract from .

Substitute the actual values of ,, and into the formula for a quadratic equation to find the resulting equation.