You are gonna need supports of some type or another. The roof will not simply cantilever out there as is, it would flex and fail in fatigue in short order I think. At a minimum you would need a horizontal frame member extending back under each roof side edge and across the rear to support the plastic. Then a diagonal strut on each side from the added rear support member going forward and down to form a triangle - that diagonal down brace, at its forward end, would probably not need to go all the way to the bottom, half way down, maybe less, would do. This brace supports the rear roof weight in compression.