Ok I got it.

I'm up to Determining Transformations and the book does a horrible horrible job of explaining. HORRIBLE

(well at least for me)

For example

Find the single transformation which maps $\displaystyle y=x^2 $ to $\displaystyle y = 2(x + 3)^2-4 $

The book tells me to assume the composition which maps $\displaystyle (x,y) \rightarrow (x',y') $

But then it says "Rearrange to make the transformation from $\displaystyle y=x^2 $ more obvious"...

Then it somehow gets $\displaystyle y=\frac{y'+4}{1} $ and $\displaystyle x=(x'+3) $

Where did the square on the (x+3) go?

Ahh I don't get it