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 .
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:


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In calculus, completing the square lets you use substitution to change integrals involving quadratics to some standard form. For example,
and or .
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Related Curriculum Standards

US Common Core State Standards, Mathematics