The recent advances in state estimation, perception, and navigation algorithms have significantly contributed to the ubiquitous use of quadrotors for inspection, mapping, and aerial imaging. To further increase the versatility of quadrotors, recent works investigated the use of an adaptive morphology, which consists of modifying the shape of the vehicle during flight to suit a specific task or environment. However, these works either increase the complexity of the platform or decrease its controllability. In this letter, we propose a novel, simpler, yet effective morphing design for quadrotors consisting of a frame with four independently rotating arms that fold around the main frame. To guarantee stable flight at all times, we exploit an optimal control strategy that adapts on the fly to the drone morphology. We demonstrate the versatility of the proposed adaptive morphology in different tasks, such as negotiation of narrow gaps, close inspection of vertical surfaces, and object grasping and transportation. The experiments are performed on an actual, fully autonomous quadrotor relying solely on onboard visual-inertial sensors and compute. No external motion tracking systems and computers are used. This is the first work showing stable flight without requiring any symmetry of the morphology.