# 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 each term.

Step 3.1.2.1

Raise to the power of .

Step 3.1.2.2

Move to the left of .

Step 3.1.2.3

Move to the left of .

Step 3.1.3

Move all terms not containing to the right side of the equation.

Step 3.1.3.1

Subtract from both sides of the equation.

Step 3.1.3.2

Subtract from both sides of the equation.

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 .

Step 3.2.2.2.1.1

Simplify each term.

Step 3.2.2.2.1.1.1

Raise to the power of .

Step 3.2.2.2.1.1.2

Move to the left of .

Step 3.2.2.2.1.1.3

Move to the left of .

Step 3.2.2.2.1.2

Simplify by adding terms.

Step 3.2.2.2.1.2.1

Subtract from .

Step 3.2.2.2.1.2.2

Subtract from .

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 .

Step 3.2.4.2.1.1

Simplify each term.

Step 3.2.4.2.1.1.1

Raise to the power of .

Step 3.2.4.2.1.1.2

Move to the left of .

Step 3.2.4.2.1.1.3

Move to the left of .

Step 3.2.4.2.1.2

Simplify by adding terms.

Step 3.2.4.2.1.2.1

Subtract from .

Step 3.2.4.2.1.2.2

Subtract from .

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

Simplify by adding terms.

Step 3.4.2.1.2.1

Add and .

Step 3.4.2.1.2.2

Add and .

Step 3.4.3

Replace all occurrences of in with .

Step 3.4.4

Simplify the right side.

Step 3.4.4.1

Simplify .

Step 3.4.4.1.1

Simplify each term.

Step 3.4.4.1.1.1

Apply the distributive property.

Step 3.4.4.1.1.2

Multiply by .

Step 3.4.4.1.1.3

Multiply by .

Step 3.4.4.1.2

Simplify by adding terms.

Step 3.4.4.1.2.1

Add and .

Step 3.4.4.1.2.2

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 3.5.3.3.2

Move the negative in front of the fraction.

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

Simplify each term.

Step 3.6.2.1.1.1

Cancel the common factor of .

Step 3.6.2.1.1.1.1

Move the leading negative in into the numerator.

Step 3.6.2.1.1.1.2

Factor out of .

Step 3.6.2.1.1.1.3

Factor out of .

Step 3.6.2.1.1.1.4

Cancel the common factor.

Step 3.6.2.1.1.1.5

Rewrite the expression.

Step 3.6.2.1.1.2

Combine and .

Step 3.6.2.1.1.3

Multiply by .

Step 3.6.2.1.1.4

Move the negative in front of the fraction.

Step 3.6.2.1.2

To write as a fraction with a common denominator, multiply by .

Step 3.6.2.1.3

Combine and .

Step 3.6.2.1.4

Combine the numerators over the common denominator.

Step 3.6.2.1.5

Simplify the numerator.

Step 3.6.2.1.5.1

Multiply by .

Step 3.6.2.1.5.2

Add and .

Step 3.6.3

Replace all occurrences of in with .

Step 3.6.4

Simplify the right side.

Step 3.6.4.1

Simplify .

Step 3.6.4.1.1

Multiply .

Step 3.6.4.1.1.1

Multiply by .

Step 3.6.4.1.1.2

Combine and .

Step 3.6.4.1.1.3

Multiply by .

Step 3.6.4.1.2

To write as a fraction with a common denominator, multiply by .

Step 3.6.4.1.3

Combine and .

Step 3.6.4.1.4

Combine the numerators over the common denominator.

Step 3.6.4.1.5

Simplify the numerator.

Step 3.6.4.1.5.1

Multiply by .

Step 3.6.4.1.5.2

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