  In the past few years, $f(Q)$ theories have drawn a lot of research attention
in replacing Einstein's theory of gravity successfully. The current study
examines the novel cosmological possibilities emerging from two specific
classes of $f(Q)$ models using the parametrization form of the equation of
state (EoS) parameter as $\omega \left( z\right) =-\frac{1}{1+3\beta \left(
1+z\right) ^{3}}$, which displays quintessence behavior with the evolution of
the Universe. We do statistical analyses using the Markov chain Monte Carlo
(MCMC) method and background datasets like Type Ia Supernovae (SNe Ia)
luminosities and direct Hubble datasets (from cosmic clocks), and Baryon
Acoustic Oscillations (BAO) datasets. This lets us compare these new ideas
about the Universe to the $\Lambda $CDM model in a number of different possible
ways. We have come to the conclusion that, at the current level of accuracy,
the values of their specific parameters are the best fits for our $f(Q)$
models. To conclude the accelerating behavior of the Universe, we further study
the evolution of energy density, pressure, and deceleration parameter for these
$f(Q)$ models.
