# Precalculus 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 .
Simplify each term.
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Multiply and .
Multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .