Many physical systems are described by quadratic equations. In such cases the requirement for a real solution is that the discriminant be non‐negative. This requirement can often lead, directly or indirectly, to maximizing or minimizing some system variable of interest. Three examples suitable for a noncalculus physics course are given : (1) projectile motion, (2) hydrostatic equilibrium (Archimedes’ principle), and (3) resistance matching.