Completing the Square
Completing the square of a quadratic function is useful for solving the equation , for plotting the graph of the function, or for finding the center of the circle (or other conic section) that is the graph of .[more]
Here is how completing the square works in words:
(1) Factor out from the first two terms, .
(2) Add the constant term in order to be able to factor as a square. Subtract from to keep equality.
(3) Factor to get the result, .
Here it is in symbols:
In calculus, completing the square lets you use substitution to change integrals involving quadratics to some standard form. For example,
and or .