Xu et al. (Eur. Phys. J. C 79 (2019) 708) have anticipated the theory of Gravity. The modified study of is elucidated here as Cosmological model. In it the action holds a role as a capricious arbitrary function . At this juncture functions as non-metricity and for matter fluid, outlines as energy-momentum tensor. The function quadratic in and linear in as has been taken as our research in which , and stand as model parameters, induced by gravity. A range of cosmological parameters have been attained by us such as in Universe viz. Hubble parameter , Friedmann–Lemaitre–Robertson–Walker (FLRW), deceleration parameter , etc. in terms of scale-factor and in terms of redshift by confining to the law of energy-conservation. The fittest values of the model parameters have been acquired by us as the observational constrictions on the model, by utilizing the accessible data sets like Hubble data sets , union compilation of SNe Ia data sets and Joint Light Curve Analysis (JLA) data sets. We have applied -test formula. The values of various observational parameters have been premeditated by us viz. , , and state finder parameters . They are absolutely very close to the standard cosmological models. It has also been observed by us that the deceleration parameter exhibits signature-flipping (transition) point within the range . It is observed that it changes its phase from decelerated to accelerated expanding universe with equation of state (EoS) for .