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OK, so what if the extra thing on Standard Parabola Guy is inside some parentheses with the x?

Like this guy:

y = ( x - 3 )^2

First of all, is this thing still a parabola?

Let's FOIL it:

y = ( x - 3 )^2 = ( x - 3 ) ( x - 3 ) = x^2 - 6x + 9 ... there's an x^2 guy... so, yes!

What's going on with the graph of this thing?

y = ( x - 3 )^2

Here's the game I play on these:

I pretend that this guy's goal in life is to be

y = ( 0 )^2

That's all he wants!

What value of x will make him happy?

y = ( x - 3 )^2 = ( 3 - 3 )^2 = ( 0 )^2 ... x = 3

So, we start him ( i.e. put the vertex ) over at x = 3 :

y = x^2

y = ( x - 3 )^2

graph of y = x^2

y = ( x - 3 )^2

 

moves Standard Parabola Guy
over to
x = 3