  In modern cosmology, the curiosity of ultimately understanding the nature of
the dark energy controlling the recent acceleration of the Universe motivates
us to explore its properties by using some novel approaches. In this work, to
explore the properties of dark energy we adopt the modified $f(Q)$ gravity
theory, where the non-metricity scalar $Q$, emerging from Weyl geometry, plays
the dynamical role. For the function $f(Q)$ we adopt the functional form
$f(Q)=Q+ 6\gamma\,H_0^2(Q/Q_0)^n$, where $n,\, \gamma,\, H_0$ and $Q_0$ are
constants. Then, we test our constructed model against the various
observational datasets, such as the Hubble, and the Pantheon+SHOES samples, and
their combined sample, through the Markov Chain Monte Carlo (MCMC) statistical
analysis. We also employ the parameter estimation technique to constrain the
free parameters of the model. In addition, we use the constrained values of the
model parameters to explore a few implications of the cosmological model. A
detailed comparison of the predictions of our model with the $\Lambda$CDM model
is also performed. In particular, we discuss in detail some cosmographic
parameters, like the deceleration, the jerk, and the snap parameters, as well
as the behavior of the dark energy and matter energy densities to see the
evolution of various energy/matter profiles. The $Om$ diagnostics is also
presented to test the dark energy nature of our model, as compared to the
standard $\Lambda$CDM paradigm. Our findings show that the considered version
of the non-metric $f(Q)$ type modified gravity theory, despite some differences
with respect to the $\Lambda$CDM paradigm, can still explain the current
observational results on the cosmological parameters, and provide a convincing
and consistent account for the accelerating expansion of the Universe.
