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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:

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

and

Contributed by: George Beck

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Common Core State Standards for Mathematics

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Completing the Square