# 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 with the solution found by solving the last equation for . In this case, the value substituted is .

Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .

Solve for in the second equation.

Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .

Solve for in the third equation.

Simplify.

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

Simplify .

Multiply and to get .

Multiply by to get .

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 to get .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by to get .

Multiply by to get .

Subtract from to get .

Reduce the expression by cancelling the common factors.

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Simplify the right side.

Simplify each term.

Simplify the numerator.

Write as a fraction with denominator .

Multiply and to get .

Multiply the numerator by the reciprocal of the denominator.

Multiply by to get .

Simplify .

Multiply and to get .

Multiply by to get .

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 to get .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by to get .

Multiply by to get .

Add and to get .

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

List the solutions to the system of equations.

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