See the picture below.
Work Step by Step
By calculating the values of $f(x)=(x-4)^2$ (with blue) and $g(x)=x^2$ (with red) we can see that for every corresponding $f(x)$ and $g(x)$ value, each x value of $g(x)$ is 4 more than the x value of $f(x)$. For drawing the exact parent graph, here is the table of values: $g(-2)= -2^2=4$ $g(-1)= -1^2=1$ $g(0)= 0^2=0$ $g(1)= 1^2=1$ $g(2)=2^2=4$ Therefore the graph of $f(x)$ is exactly the same as the graph of $g(x)=x^2$ but translated 4 units right. For drawing the exact graph of $f(x)$ here is the table of values of the given function: $f(2)=(2-4)^2=4$ $f(3)=(3-4)^2=1$ $f(4)=(4-4)^2=0$ $f(5)=(5-4)^2=1$ $f(6)=(6-4)^2=4$