We develop a curved Koszul duality theory for algebras presented by quadratic-linear-constant relations over binary unital operads. As an application , we study Poisson n-algebras given by polynomial functions on a standard shifted symplectic space. We compute explicit resolutions of these algebras using curved Koszul duality. We use these resolutions to compute derived enveloping algebras and factorization homology on parallelized simply connected closed manifolds of these Poisson n-algebras.