In this talk, we will establish that the theory of symmetric Macdonald polynomials aligns with quantum and affine Schubert calculus using a discovery that distinguished weak chains can be identified by chains in the strong (Bruhat) order poset on the type-A affine Weyl group. We will construct two one- parameter families of symmetric functions that respectively transition positively with Hall-Littlewood and Macdonald's P-functions, and specialize to the representatives for Schubert classes of homology and cohomology of the affine Grassmannian. Our approach will lead us to conjecture that all elements in a defining set of 3-point genus 0 Gromov-Witten invariants for flag manifolds can be formulated as strong covers.