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Graphing by Completing the Square - Freaky Things That Can Happen

Let's walk through another one:

y = -2x^2 + 12x - 13

STEP 1:

y = -2x^2 + 12x - 13 ... Do not touch the -13!

STEP 2: Factor out the trouble-maker:

y = -2 ( x^2 - 6x ) -13 ... Careful here! Watch your signs!

*Just distribute back through to check.

STEP 3:

y = -2 ( x^2 - 6x ___ ) - 13 ___

STEP 4:

y = -2 ( x^2 - 6x ___ ) - 13 ___ ... 1/2 ( -6 ) = -3 ... -3 is circled guy

STEP 5:

y = -2 ( x^2 - 6x + 9 ) - 13 ___ ... ( 3 )^2 = 9 ( circled guy squared )

STEP 6:

y = -2 ( x^2 - 6x + 9 ) - 13 + 18 ... the -2 distributes to the +9 to give -18 ... undo it with the +18

STEP 7:

y = -2 ( x - 3 )^2 + 5

I'll let you check it by multiplying it out.

And graph it!

YOUR TURN:

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

2x^2 + 20x + 43

y = -5x^2 - 20x - 17