The graph of f(x) = x2 has been shifted into the form f(x) = (x − h)2 + k.

what is the value of k?

My solution to the problem is as follows:

y=x^2 touch origin
 
now it is shifted to (4,5)

so new equation will be:
 
f(x)-5 = (x-4)2

f(x)= (x-4)2 + 5
     
so k=5

I hope my answer has come to your help. God bless and have a nice day ahead!