  This paper explores the relationship between mirror symmetry for P^2, at the
level of big quantum cohomology, and tropical geometry. The mirror of P^2 is
typically taken to be ((C^*)^2,W), where W is a Landau-Ginzburg potential of
the form x+y+1/xy. The complex moduli space of the mirror is the universal
unfolding of W, and oscillatory integrals produce a Frobenius manifold
structure on this universal unfolding. We show that W can be deformed by
counting Maslov index two tropical disks, and the natural paramaters appearing
in this deformation are then the flat coordinates on the moduli space.
Furthermore, the oscillatory integrals are shown to read off directly tropical
curve counts from the potential. Thus we show in fact that mirror symmetry for
P^2 is equivalent in a strong sense to tropical curve counting formulas,
including tropical formulas for gravitational descendent invariants.
