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Algebra Difficulty 3.0 AMC 10/12 Find the answer Canada

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

(A) $9$ (B) $32$ (C) $33$ (D) $36$ (E) $37$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.