Collision avoidance maneuvers using braking and steering provide opportunities to avoid a collision at higher velocities compared to braking or steering only. This work investigates control concepts with integrated trajectory planning for combined braking and steering maneuvers using model predictive control (MPC) approaches. A major challenge here is the computational efficiency of the optimization process accounting for nonlinear constraints or nonlinear dynamic models. The main contribution of this work is the introduction of several simplifications which reduces the nonlinear optimization problem to a quadratic program and thus enables application in a vehicle demonstrator. Comparison of the quadratic MPC with the nonlinear MPC shows not only similar performance in a simulation environment, but demonstrates strongly reduced computation time by a factor of approximately 400.