  In this article we focus on the study of special parabolic points in surfaces
arising as graphs of polynomials, we give a theorem of Viro's patchworking type
to build families of real polynomials in two variables with a prescribed number
of special parabolic points in their graphs. We use this result to build a
family of degree d real polynomials in two variables with $(d-4)(2d-9)$ special
parabolic points in its graph. This brings the number of special parabolic
points closer to the upper bound of $(d-2)(5d-12)$ when $d \geq 13$, which is
the best known up until now.
