I get why you can move the curve for (a*(x-b))^2 where ever you want horizontally and then stretch as you want and it stays in the same place. Why does (ax-b)^2 behave any differently(and rather weirdly)?
I get how the parentheses force the order in the first one. I want to know the reasoning behind why the second one functions (pun intended) the way it does. Please explain in as detail and verbosely as you wish. Thanks.
The second function could also be written as
$$\left(a\left(x-\frac{b}{a}\right)\right)^2$$ if you want to put it into a form that is similar to the first one.