  We develop a curved Koszul duality theory for algebras presented by
quadratic-linear-constant relations over unital versions of binary quadratic
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 with coefficients in these
Poisson $n$-algebras.
