The present work is in a context of derivative-free optimization involving direct search algorithms guided by surrogate models of the original problem. These models are classified into two categories: static surrogates and dynamic models. This work introduces the quadratic hybrid model (HQM), that dynamically corrects information from a static surrogate. Instead of bringing an additive or multiplicative correction, the HQM generalizes these two types of corrections by considering the static model as an input variable of the quadratic model. Numerical tests are performed with the Mads algorithm on three multidisciplinary and one simulation-based engineering problems. The results show that the contribution of the HQM to the Mads algorithm is to solve problems at greater precision for the same computational budget.