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Minima and Maxima of Quadratics

To find the minimum or maximum of a quadratic we complete the square expressing the function in the form

Ifthe minimum will be wheresoand the minimum is at

Ifthe maximum will be wheresoand the maximum is at

For example, to find the minimum ofcomplete the square to getthen the minimum is at

To find the maximum ofcomplete the square to get  then the maximum is at