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Graphing by Completing the Square - How

STEP 6: Finish it off:

y = ( x^2 + 10x + 25 ) - 28

Go back and get circled guy.

y = ( x + 5 )^2 - 28 ... +5 is the circled guy

We're all done and can now graph this guy.

y = ( x + 5 )^2 - 28 ... x = -5 , down 28, left 5

We can always check our answers on these by multiplying them back out!

y = ( x + 5 )^2 - 28 = ( x + 5 ) ( x + 5 ) - 28 = x^2 + 10x + 25 - 28 = x^2 + 10x - 3 ... Yep!

Let's do another one:

y = x^2 - 6x + 3

STEP 1:

y = x^2 - 6x + 3 ... do not touch the +3 !

STEP 2:

y = ( x^2 - 6x ____ ) + 3 ____
 

STEP 3:

y = ( x^2 - 6x ____ ) + 3 ____ ... ( 1/2 ) ( -6 ) = -3 ( circled guy )