# Algebra 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 .

Simplify.

Remove parentheses.

Remove parentheses.

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 the right side.

Simplify terms.

Simplify each term.

Move the negative in front of the fraction.

Simplify .

Multiply by to get .

Multiply by to get .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by to get .

Subtract from to get .

Divide by to get .

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.