Graph shifts - fatter, skinnier parabola

GRE Quant Problem Solving
1

Hi, can anyone explain me the theory behind the following
When you have y=x^2 and you make it y=2x^2 the parabola becomes skinnier
My logic was that it would become fatter because for every y you have twice the x value squared but it’s the opposite and I don’t get it. Thanks

2

The key idea is that when you change from y = x2 to y = 2x2, the x value required to get a corresponding y-value decreases. For example, if y = 5, x reduces from \sqrt{5} to \sqrt{2.5}. That is why you exhibit the “skinny” property.

You need the reverse to happen if you want the graph to get “fatter”.

3

thanks! this way i can memorize/understand it better, thanks a million :slight_smile:

probably i’m making the standard mistake my misinterpreting y = 2x, indeed it means x is smaller and y is bigger.