# 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 the system of equations to find the values of , , and .
Simplify each equation.
Remove parentheses.
Simplify .
Simplify each term.
Raising to any positive power yields .
Multiply by .
Multiply by .
Combine the opposite terms in .
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.
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 .
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.
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.