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Graphing by Completing the Square - Freaky Things That Can Happen

Here's another creepy guy...  He looks so easy, but students tend to mess him up.

y = -x^2 + 12x - 32
Just an innocent looking -1 in front...

We just have to be extra careful with the signs!

STEP 1:

y = -x^2 + 12x - 32 ... do not touch the -32!

STEP 2: Factor out the trouble-maker:

y = - ( x^2 - 12x ) - 32 ... watch the sign on the 12x!

STEP 3:

y = - ( x^2 - 12x ___ ) - 32 ___

STEP 4:

y = - ( x^2 - 12x ___ ) - 32 ___ ... 1/2 ( -12 ) = -6 ... -6 is circled guy

STEP 5:

y = - ( x^2 - 12x + 36 ) - 32 ___ ... ( -6 )^2 = 36

STEP 6:

y = - ( x^2 - 12x + 36 ) - 32 + 36 ... the negative sign distributes to the 36 to give -36 ... undo it with the +36

STEP 7:

y = - ( x - 6 )^2 + 4 ... -6 is circled guy

Check it and graph it!

TRY IT:

Complete the square... check by multiplying them back out... and graph:

y = -x^2 - 6x - 11