Question

what does the four stand for in y=4(x-1.5)^2

Answer 1

its a 'multiplier' or a 'scaler' it will make the parabola either wider or narrower.

Answer 2

Yes. As opposed to y=(x-1.5)^2, y=4(x-1.5)^2 will have a much narrower graph. on the other hand, y=(1/4)(x-1.5)^2 would have a much wider graph.