<p>This study investigates the impact of horizontal throughflow on the linear stability of thermogravitational penetrative convection in a vertical porous layer saturated with a fluid whose density obeys a general quadratic dependence on temperature. The resulting eigenvalue problem is solved numerically by employing the Chebyshev collocation method. The analysis reveals that the onset of instability is governed solely by the combined action of the density-maximum property and the Prandtl–Darcy number. Throughflow cannot trigger instability—either on its own or when acting with only one of these mechanisms—and its primary role is to reshape the stability landscape once instability has developed. A key finding is that the coupling between throughflow and the general quadratic density law yields closed neutral stability curves and requires two distinct Darcy–Rayleigh numbers to demarcate the stability boundaries—an uncommon feature in single-component diffusive systems. Furthermore, the basic flow is shown to be unconditionally stable for Prandtl–Darcy numbers exceeding 7.087772, independent of all other governing parameters.</p>