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

The key idea is that when you change from y = x^{2} to y = 2x^{2}, 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”.

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

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