Roughly speaking, a hypersurface defined by a polynomial with coefficients in a formal power series ring is called quasi-ordinary if the discriminant of the polynomial is a monomial. I will discuss a criterion that provides whether a given irreducible hypersurface is quasi-ordinary. This involves weighted polyhedra and embeddings in higher dimensional ambient spaces such that the original hypersurface may be considered as an overweight deformation of a variety defined by binomial ideal.