The notion of convexity of vector spaces can be generalized to dimension-free sets of matrices. A natural question that then arises is how to identify a set's matrix convex hull. We introduce some techniques for getting a grasp on the matrix convex hull of semi-algebraic sets and look at one of these in particular: The bent TV screen. This is the set $$ \{ (X, Y) : I - X^2 - Y^4 \succeq 0 \} $$ It is convex in the scalar case but is not matrix convex. In fact, there is no known "simple" formula for its matrix convex hull.