A new <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e911" altimg="si5.svg"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>Q</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> cosmological model with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e924" altimg="si216.svg"><mml:mrow><mml:mi>H</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> quadratic…

We present a new $f(Q)$ cosmological model capable of reproducing late-time acceleration, i.e. $f\left( Q\right) = \lambda_{0}\left( \lambda +Q\right) ^{n}$ by supporting certain parametrization the Hubble parameter. By using observational data from Hubble, Pantheon, and Baryonic Acoustic Oscillations (BAO) dataset, we investigate constraints on proposed quadratic parameter $H(z)$. This proposal caused Universe to transition its decelerated phase accelerated phase. Further, current constrained value deceleration combined Hubble+Pantheon+BAO dataset is $q_{0}=-0.285\pm 0.021$, which indicates that accelerating. also analyze evolution energy density, pressure, EoS parameters infer Universe's accelerating behavior. Finally, use stability analysis with linear perturbations assure model's stability.