# 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.

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.

Raise to the power of .

Move to the left of .

Move to the left of .

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 second 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 .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify each term.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Replace all occurrences of in with .

Simplify .

Simplify each term.

Apply the distributive property.

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Simplify by adding terms.

Subtract from .

Add and .

Solve for in the third 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 .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Replace all occurrences of in with .

Simplify .

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

Multiply .

Multiply and .

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 .

Multiply and .

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

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