  Given a compact polarized K\"ahler manifold $X\hookrightarrow\mathbb{CP}^N$,
the space of Bergman metrics on $X$, parameterized by
$\mathrm{SL}(N+1,\mathbb{C})$, corresponds to a dense set in the space of
K\"ahler potentials in the K\"ahler class as $N\to\infty$. Critical points of
the $k$th K-energy functional, which is defined on the K\"ahler class,
correspond to metrics with harmonic $k$th Chern form. In this paper it is shown
that the higher K-energy functionals, when restricted to the Bergman metrics,
are expressible as the energies of certain pairs of vectors (tensors products
of discriminants). Consequentially, we obtain results on the asymptotic
behavior of these functionals along 1-parameter subgroups and their boundedness
properties.
