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 the system of equations to find the values of , , and .
Tap for more steps...
Step 3.1
Solve for in .
Tap for more steps...
Step 3.1.1
Rewrite the equation as .
Step 3.1.2
Simplify each term.
Tap for more steps...
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.
Tap for more steps...
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.
Tap for more steps...
Step 3.2.1
Replace all occurrences of in with .
Step 3.2.2
Simplify .
Tap for more steps...
Step 3.2.2.1
Simplify the left side.
Tap for more steps...
Step 3.2.2.1.1
Remove parentheses.
Step 3.2.2.2
Simplify the right side.
Tap for more steps...
Step 3.2.2.2.1
Simplify .
Tap for more steps...
Step 3.2.2.2.1.1
Simplify each term.
Tap for more steps...
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.
Tap for more steps...
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 .
Tap for more steps...
Step 3.2.4.1
Simplify the left side.
Tap for more steps...
Step 3.2.4.1.1
Remove parentheses.
Step 3.2.4.2
Simplify the right side.
Tap for more steps...
Step 3.2.4.2.1
Simplify .
Tap for more steps...
Step 3.2.4.2.1.1
Simplify each term.
Tap for more steps...
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.
Tap for more steps...
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 .
Tap for more steps...
Step 3.3.1
Rewrite the equation as .
Step 3.3.2
Move all terms not containing to the right side of the equation.
Tap for more steps...
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.
Tap for more steps...
Step 3.4.1
Replace all occurrences of in with .
Step 3.4.2
Simplify the right side.
Tap for more steps...
Step 3.4.2.1
Simplify .
Tap for more steps...
Step 3.4.2.1.1
Simplify each term.
Tap for more steps...
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.
Tap for more steps...
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.
Tap for more steps...
Step 3.4.4.1
Simplify .
Tap for more steps...
Step 3.4.4.1.1
Simplify each term.
Tap for more steps...
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.
Tap for more steps...
Step 3.4.4.1.2.1
Add and .
Step 3.4.4.1.2.2
Add and .
Step 3.5
Solve for in .
Tap for more steps...
Step 3.5.1
Rewrite the equation as .
Step 3.5.2
Move all terms not containing to the right side of the equation.
Tap for more steps...
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.
Tap for more steps...
Step 3.5.3.1
Divide each term in by .
Step 3.5.3.2
Simplify the left side.
Tap for more steps...
Step 3.5.3.2.1
Cancel the common factor of .
Tap for more steps...
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.
Tap for more steps...
Step 3.5.3.3.1
Cancel the common factor of and .
Tap for more steps...
Step 3.5.3.3.1.1
Factor out of .
Step 3.5.3.3.1.2
Cancel the common factors.
Tap for more steps...
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.
Tap for more steps...
Step 3.6.1
Replace all occurrences of in with .
Step 3.6.2
Simplify the right side.
Tap for more steps...
Step 3.6.2.1
Simplify .
Tap for more steps...
Step 3.6.2.1.1
Simplify each term.
Tap for more steps...
Step 3.6.2.1.1.1
Cancel the common factor of .
Tap for more steps...
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.
Tap for more steps...
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.
Tap for more steps...
Step 3.6.4.1
Simplify .
Tap for more steps...
Step 3.6.4.1.1
Multiply .
Tap for more steps...
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.
Tap for more steps...
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
Enter YOUR Problem
Mathway requires javascript and a modern browser.