  In this exclusive study of the modified $f(Q)$ theory of gravity in the open
and closed type Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe model, we
impose some constraints from the classical energy conditions. The viable range
of parameter $\beta$ for two different $f(Q)$ models, $f(Q)=Q+\beta Q^2$ and
$f(Q)=Q+\beta\sqrt{-Q}$, are analyzed in details and the related cosmological
implications are discussed. Violation of effective strong energy condition is
resulting into late-time acceleration of the Universe. Present observational
values of Hubble parameter and deceleration parameter are used to constrain the
parameters.
