Function Transformations / Translations: Additional Rules

It mentions "The parabola for 2x^{2}grows twice as fast asx^{2}, so its graph is tall and skinny. On the other hand, the parabola for the function (^{1}/_{2})x^{2}grows only half as fast, so its graph is short and fat.".

How come the parabola for 2x^{2}is tall and skinny? Aren't both the parabola for 2x^{2}and (^{1}/_{2})xof the same "height"? (Are they both go to infinity?) So why is the parabola for 2^{2}x^{2}tall and the parabola for(^{1}/_{2})xshort?^{2}