  The shape of the primordial matter power spectrum Plin(k) encodes critical
information on cosmological parameters. At large scales, the observable galaxy
power spectrum Pobs(k) is expected to follow the shape of Plin(k), but on
smaller scales the effects of nonlinearity and galaxy bias make the ratio
Pobs(k)/Plin(k) scale-dependent. We develop a method that can extend the
dynamic range of the Plin(k) recovery by incorporating constraints on the
galaxy halo occupation distribution (HOD) from the projected galaxy correlation
function wp. We devise an analytic model to calculate Pobs(k) in real-space and
redshift-space. Once HOD parameters are determined by matching wp for a given
cosmological model, galaxy bias is completely specified, and our analytic model
predicts both the shape and normalization of Pobs(k). Applying our method to
SDSS main galaxy samples, we find that the real-space Pobs(k) follows the shape
of the nonlinear matter power spectrum at the 1-2% level up to k=0.2 h/Mpc.
When we apply our method to SDSS LRG samples, the linear bias approximation is
accurate to 5% at k<0.08 h/Mpc, but the scale-dependence of LRG bias prevents
the use of linear theory at k>0.08 h/Mpc. Our HOD model prediction is in good
agreement with the recent SDSS LRG Pobs(k) measurements at all measured scales
(k<0.2 h/Mpc), naturally explaining the shape of Pobs(k). The "Q-model"
prescription is a poor description of galaxy bias for the LRG samples, and it
can lead to biased cosmological parameter estimates when measurements at k>0.1
h/Mpc are included in the analysis. We quantify the potential bias and
constraints on cosmological parameters that arise from applying linear theory
and Q-model fitting, and we demonstrate the utility of HOD modeling of future
high precision measurements of Pobs(k) on quasi-linear scales.
