# 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.

Solve for in the first equation.

Replace all occurrences of in with

Replace all occurrences of in with

Solve for in the second equation.

Replace all occurrences of in with

Replace all occurrences of in with

Solve for in the third equation.

Replace all occurrences of in with

Replace all occurrences of in with

Simplify.

Simplify .

Divide by .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Simplify .

Simplify each term.

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Multiply by .

Multiply by .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

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.