We consider the free additive convolution of two probability measures mu and nu on the real line and show that mu boxed plus nu is supported on a single interval if mu and nu each has single interval support. Moreover, the density of mu boxed plus nu is proven to vanish as a square root near the edges of its support if both mu and nu have power law behavior with exponents between -1 and 1 near their edges. In particular, these results show the ubiquity of the conditions in our recent work on optimal local law at the spectral edges for addition of random matrices [5].