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

For this case, the parent function is given by:
 
 We apply the following transformation:
 Expansions and horizontal compressions:
 The graph of y = f (bx):
 If 0 <b <1, the graph of y = f (x) expands horizontally by the factor of 1 / b. (It lengthens)
 Applying the transformation we have:
 
 Therefore, the stretch factor is 4, due to:
 
 Rewriting:
 
 
 the equation of the new function is: