Algebra 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 for in .
Rewrite the equation as .
Simplify .
Simplify each term.
Raising to any positive power yields .
Multiply by .
Add and .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify .
Simplify the left side.
Remove parentheses.
Simplify the right side.
Simplify each term.
Raise to the power of .
Move to the left of .
Move to the left of .
Replace all occurrences of in with .
Simplify the left side.
Remove parentheses.
Solve for in .
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 with in each equation.
Replace all occurrences of in with .
Simplify the right side.
Simplify .
Simplify each term.
Apply the distributive property.
Multiply by .
Multiply by .
Simplify by adding terms.
Add and .
Add and .
Solve for in .
Rewrite the equation as .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
Add and .
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Divide by .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify the right side.
Simplify .
Multiply by .
Subtract from .
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