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Graphing by Completing the Square - Intro

But, first, I need to remind you what a "square" is -- actually, a perfect square.  Remember when we were factoring ( or solving ) and we'd get something like this?

x^2 + 4x + 4 = ( x + 2 ) ( x + 2 )

Well, just like we can write  b b  as   b^2 , we can write

( x + 2 ) ( x + 2 ) = ( x + 2 )^2 ... it's a square!

Here are some perfect square quadratics:

y = x^2 + 6x + 9 = ( x + 3 ) ( x + 3 ) = ( x + 3 )^2

y = x^2 - 8x + 16 = ( x - 4 ) ( x - 4 ) = ( x - 4 )^2

y = x^2 + 5x + 25/4 = ( x + 5/2 ) ( x + 5/2 ) = ( x + 5/2 )^2

We'll be aiming for guys like these in our trick.  Go to the next lesson to see how it works.