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We develop a curved Koszul duality theory for algebras presented byquadratic-linear-constant relations over unital versions of binary quadraticoperads. As an application, we study Poisson $n$-algebras given by polynomialfunctions on a standard shifted symplectic space. We compute explicitresolutions of these algebras using curved Koszul duality. We use theseresolutions to compute derived enveloping algebras and factorization homologyon parallelized simply connected closed manifolds with coefficients in thesePoisson $n$-algebras.

Curved Koszul duality of algebras over unital versions of binary operads