The Gauss-Lucas Theorem is a classical complex analysis result that states the critical points of a single-variable complex polynomial lie inside the closed convex hull of the zeros of the polynomial. Although the result is well-known, it is not typically presented in a first course in complex analysis. The ease with which modern technology allows the plotting of zeros and critical points makes the result discoverable by students. We propose a visual investigation, followed by a series of exercises leading to different complete proofs of the theorem.