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Completing the Square

Mathematics & Statistic Tutor Perth - SPSS Help   

Completing the Square

This is a technique that takes any quadratic expression  rearranges to be a perfect square in doing so you will have subtract a portion.  This portion is what you have added to make it a perfect square.
Examples of perfect squares    
32

(x+1)2

(3x4 - 8)2

sin2 (x)

It is often known as the turning point form of a quadratic;
 if the expression is written with a minus sign (in the yellow box) then
the value of p (in the red box) and
the value of q (in the blue box)
are the x and y coordinates of the turning point.

The turning point of this quadratic is:

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