You are right that the next step is vertical compression by 4 (i.e., multiplying y by 1/4).

Maybe it'shorizontal expansionby 2? If , then , i.e., the graph of is obtained from the graph of f(x) by changing each (x, y) into (2x, y).

In other words, compressing the parabola vertically by 4 and expanding it horizontally by 2 give the same result.