To complete the table for the function \( f(x) = x^2 \), we will calculate \( f(x) \) for each given value of \( x \).
\[ \begin{array}{|c|c|} \hline x & f(x) = x^2 \ \hline -4 & (-4)^2 = 16 \ -2 & (-2)^2 = 4 \ 0 & (0)^2 = 0 \ 2 & (2)^2 = 4 \ \hline \end{array} \]
So the completed table is:
\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline -4 & 16 \ -2 & 4 \ 0 & 0 \ 2 & 4 \ \hline \end{array} \]