# Algebra Examples

, ,
Use the standard form of a quadratic equation as the starting point for finding the equation through the three points.
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.
Solve the system of equations to find the values of ,, and .
Solve for in the first equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Simplify.
Remove parentheses.
Remove parentheses.
Solve for in the second equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Solve for in the third equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Simplify the right side.
Simplify terms.
Simplify each term.
Move the negative in front of the fraction.
Simplify .
Multiply by to get .
Multiply by to get .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by to get .
Subtract from to get .
Divide by to get .
List the solutions to the system of equations.
Substitute the actual values of ,, and into the formula for a quadratic equation to find the resulting equation.

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