If you horizontally stretch the quadratic parent function,  f(x) =  x2, by a factor of 4, what is the equation of the new function?

Please write x^2, not x2.

If you stretch the graph of y=x^2 vertically by a factor of 4, the resulting graph represents the quadratic function y = 4x^2.  It's still a parabola, but appears to be thinner.

This particular question is about horizontal stretching, however.  Stretching the graph horizontally by a factor of 4 results in the new function g(x) = (x/4)^2.  Try graphing x^2 and also (x/4)^2 on the same set of axes to observe this phenomenon.