Let's plot the graph of each function to be able to determine the order from the narrowest to the widest graph.
From the graph that represents each of the functions, it appears that g(x) = 4x^2 is the narrowest and f(x) =1/2x^2 is the widest graph.
Therefore, the order of the functions, from narrowest to widest, will be:
g(x) = 4x^2, h(x) = -3x^2, f(x) =1/2x^2