From the problem, we have a function of x :
[tex]f(x)=(x+7)^2[/tex]
From the graph, g(x) is the result when f(x) is shifted 2 units downward, and note that when shifting a function f(x) c units downward, the function will be :
[tex]f(x)\rightarrow f(x)-c[/tex]
Since f(x) will be shifted 2 units downward, the function will be :
[tex]\begin{gathered} g(x)=f(x)-2 \\ g(x)=(x+7)^2-2 \end{gathered}[/tex]
The answer is D. g(x) = (x + 7)^2 - 2
