# 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

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

Add and .

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 .

Step 3.2.4.1

Simplify the left side.

Step 3.2.4.1.1

Remove parentheses.

Step 3.2.4.2

Simplify the right side.

Step 3.2.4.2.1

Simplify each term.

Step 3.2.4.2.1.1

Raise to the power of .

Step 3.2.4.2.1.2

Move to the left of .

Step 3.2.4.2.1.3

Move to the left of .

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

Add to both sides of the equation.

Step 3.3.2.2

Subtract from both sides of the equation.

Step 3.3.2.3

Combine the opposite terms in .

Step 3.3.2.3.1

Subtract from .

Step 3.3.2.3.2

Add and .

Step 3.3.3

Divide each term in by and simplify.

Step 3.3.3.1

Divide each term in by .

Step 3.3.3.2

Simplify the left side.

Step 3.3.3.2.1

Cancel the common factor of .

Step 3.3.3.2.1.1

Cancel the common factor.

Step 3.3.3.2.1.2

Divide by .

Step 3.3.3.3

Simplify the right side.

Step 3.3.3.3.1

Cancel the common factor of and .

Step 3.3.3.3.1.1

Factor out of .

Step 3.3.3.3.1.2

Cancel the common factors.

Step 3.3.3.3.1.2.1

Factor out of .

Step 3.3.3.3.1.2.2

Cancel the common factor.

Step 3.3.3.3.1.2.3

Rewrite the expression.

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

Cancel the common factor of .

Step 3.4.2.1.1.1

Factor out of .

Step 3.4.2.1.1.2

Cancel the common factor.

Step 3.4.2.1.1.3

Rewrite the expression.

Step 3.4.2.1.2

Add and .

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

Subtract from both sides of the equation.

Step 3.5.2.2

Subtract from .

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

Cancel the common factor of and .

Step 3.5.3.3.1.1

Factor out of .

Step 3.5.3.3.1.2

Cancel the common factors.

Step 3.5.3.3.1.2.1

Factor out of .

Step 3.5.3.3.1.2.2

Cancel the common factor.

Step 3.5.3.3.1.2.3

Rewrite the expression.

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 the numerator by the reciprocal of the denominator.

Step 3.6.2.1.2

Multiply .

Step 3.6.2.1.2.1

Multiply by .

Step 3.6.2.1.2.2

Multiply by .

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