ما معنى Quadratic approximation؟

The quadratic approximation of Barone-Adesi and Whaley writes the American value as the European value plus a premium of the form $A(S/S^*)^{q}$, where the exponent $q$ solves the quadratic that the time-independent part of the pricing equation imposes, and the critical spot $S^*$ is found numerically from value matching and smooth pasting at $S^*$. Beyond $S^*$ the option is worth its exercise value.