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Graphing by Completing the Square - How

STEP 3:

y = ( x^2 + 10x ____ ) - 3 ____ ... take half of 10x and put a circle around him: 1/2 ( 10 ) = 5 ... 5 is circled guy
 

STEP 4:  Square circled guy...

y = ( x^2 + 10x + 25 ) - 3 ____ ( 5 )^2 = 25 ... and put it here
 

STEP 5: THIS IS THE MOST FORGOTTEN STEP!

Remember that equations are like see-saws...  We have to keep them balanced!

We just plopped 25 pounds onto the right side of the equation:

y = ( x^2 + 10x + 25 ) - 3 ____ ... the right side is heavier

So...  we'll just take it back off!

y = ( x^2 + 10x + 25 ) - 3 - 25

*That's why I had you put a blank at the end...
So you wouldn't forget this!