2008 Fermat Problem 22

For how many integers k do the parabolas with equations y=-\frac{1}{8}x^2+4 and y=x^2-k intersect on or above the x-axis?

\textbf{(A)}\ 9\quad \textbf{(B)}\ 32\quad \textbf{(C)}\ 33\quad \textbf{(D)}\ 36\quad \textbf{(E)}\ 37

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