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In this paper, we investigate the modified symmetric teleparallel gravity or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity, where <i>Q</i> is the nonmetricity, to study the evolutionary history of the universe by considering the functional form of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mrow><mo>(</mo><mi>Q</mi><mo>)</mo></mrow><mo>=</mo><mi>α</mi><msup><mi>Q</mi><mi>n</mi></msup></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and <i>n</i> are constants. Here, we consider the parametrization form of the deceleration parameter as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>=</mo><msub><mi>q</mi><mn>0</mn></msub><mo>+</mo><mrow><msub><mi>q</mi><mn>1</mn></msub><mspace width="0.166667em"></mspace><mi>z</mi></mrow><mo>/</mo><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>z</mi><mo>)</mo></mrow><mn>2</mn></msup></mrow></semantics></math></inline-formula> (with the parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>q</mi><mn>0</mn></msub></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi></mrow></semantics></math></inline-formula> at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>z</mi><mo>=</mo><mn>0</mn><mo>)</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>q</mi><mn>1</mn></msub></semantics></math></inline-formula>, and the redshift, <i>z</i>), which provides the desired property for a sign flip from a decelerating to an accelerating phase. We obtain the solution of the Hubble parameter by examining the mentioned parametric form of <i>q</i>, and then we impose the solution in Friedmann equations. Employing the Bayesian analysis for the Observational Hubble data (OHD), we estimated the constraints on the associated free parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>H</mi><mn>0</mn></msub><mo>,</mo><msub><mi>q</mi><mn>0</mn></msub><mo>,</mo><msub><mi>q</mi><mn>1</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mn>0</mn></msub></semantics></math></inline-formula> the current Hubble parameter to determine if this model may challenge the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">Λ</mi></semantics></math></inline-formula>CDM (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">Λ</mi></semantics></math></inline-formula> cold dark matter with the cosmological constant, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">Λ</mi></semantics></math></inline-formula>) limitations. Furthermore, the constrained current value of the deceleration parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>q</mi><mn>0</mn></msub><mo>=</mo><mo>−</mo><mn>0</mn><mo>.</mo><msubsup><mn>832</mn><mrow><mo>−</mo><mn>0.091</mn></mrow><mrow><mo>+</mo><mn>0.091</mn></mrow></msubsup></mrow></semantics></math></inline-formula> shows that the present universe is accelerating. We also investigate the evolutionary trajectory of the energy density, pressure, and EoS (equation-of-state) parameters to conclude the accelerating behavior of the universe. Finally, we try to demonstrate that the considered parametric form of the deceleration parameter is compatible with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity.