# Precalculus Examples

, ,
Step 1
Use the standard form of a quadratic equation as the starting point for finding the equation through the three points.
Step 2
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.
Step 3
Solve the system of equations to find the values of , , and .
Step 3.1
Solve for in .
Step 3.1.1
Rewrite the equation as .
Step 3.1.2
Simplify .
Step 3.1.2.1
Simplify each term.
Step 3.1.2.1.1
Raising to any positive power yields .
Step 3.1.2.1.2
Multiply by .
Step 3.1.2.2
Step 3.2
Replace all occurrences of with in each equation.
Step 3.2.1
Replace all occurrences of in with .
Step 3.2.2
Simplify .
Step 3.2.2.1
Simplify the left side.
Step 3.2.2.1.1
Remove parentheses.
Step 3.2.2.2
Simplify the right side.
Step 3.2.2.2.1
Simplify each term.
Step 3.2.2.2.1.1
Raise to the power of .
Step 3.2.2.2.1.2
Move to the left of .
Step 3.2.2.2.1.3
Move to the left of .
Step 3.2.3
Replace all occurrences of in with .
Step 3.2.4
Simplify the left side.
Step 3.2.4.1
Remove parentheses.
Step 3.3
Solve for in .
Step 3.3.1
Rewrite the equation as .
Step 3.3.2
Move all terms not containing to the right side of the equation.
Step 3.3.2.1
Subtract from both sides of the equation.
Step 3.3.2.2
Subtract from both sides of the equation.
Step 3.3.2.3
Subtract from .
Step 3.4
Replace all occurrences of with in each equation.
Step 3.4.1
Replace all occurrences of in with .
Step 3.4.2
Simplify the right side.
Step 3.4.2.1
Simplify .
Step 3.4.2.1.1
Simplify each term.
Step 3.4.2.1.1.1
Apply the distributive property.
Step 3.4.2.1.1.2
Multiply by .
Step 3.4.2.1.1.3
Multiply by .
Step 3.4.2.1.2
Step 3.4.2.1.2.1
Step 3.4.2.1.2.2
Step 3.5
Solve for in .
Step 3.5.1
Rewrite the equation as .
Step 3.5.2
Move all terms not containing to the right side of the equation.
Step 3.5.2.1
Add to both sides of the equation.
Step 3.5.2.2
Step 3.5.3
Divide each term in by and simplify.
Step 3.5.3.1
Divide each term in by .
Step 3.5.3.2
Simplify the left side.
Step 3.5.3.2.1
Cancel the common factor of .
Step 3.5.3.2.1.1
Cancel the common factor.
Step 3.5.3.2.1.2
Divide by .
Step 3.5.3.3
Simplify the right side.
Step 3.5.3.3.1
Divide by .
Step 3.6
Replace all occurrences of with in each equation.
Step 3.6.1
Replace all occurrences of in with .
Step 3.6.2
Simplify the right side.
Step 3.6.2.1
Simplify .
Step 3.6.2.1.1
Multiply by .
Step 3.6.2.1.2
Subtract from .
Step 3.7
List all of the solutions.
Step 4
Substitute the actual values of ,, and into the formula for a quadratic equation to find the resulting equation.
Step 5