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Here we go!

 

Let's turn this guy:

 

  y = x^2 + 10x - 3

 

into this form: 

  y = a ( x - h )^2 + k

This is a trick -- it's just a few steps to go through...  and it will ALWAYS work.  This is one of the few times I will be telling you that this is just a process to memorize.  It's a zero-thinking process.  Go into robot mode!  If you know how to do it, it's a snap -- a slam dunk.  If you don't know how to do it, you have NO hope of getting it right.  There's no way to guess or fudge your way through this one!

Let's do it!

y = x^2 + 10x - 3

STEP 1:  Put a box around the last guy...

y = x^2 + 10x - 3

and say out loud, "Do not touch the -3 !"
( You'll thank me for this later. )
 

STEP 2:  Put some ( ) and ____ in like this:

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