the graph of which of the following equations would be the narrowest parabola?

y = -2x 2
y = -x 2
y = x 2
y = x 2

The narrowest parabola will be the one with the greatest magnitude of acceleration...y, dy/dx, d2y/dx2 for each are:

-2x^2, -4x, -4

-x^2, -2x, -2

x^2, 2x, 2  and your fourth equation is the same as the third?

From what you have the first equation, -2x^2, will be the narrowest because it has the greatest magnitude of acceleration |-4|=4

For being nice i appreciate it but abc