When polishing the mandibular arch, the patient's chin should be _____ and the chin should be _____ for the maxillary.

When polishing the mandibular arch, the proper position for the patient's chin should be directed downwards. This positioning allows for better access to the posterior teeth and the overall arch, making it easier for the dental assistant to effectively polish the surfaces. For the maxillary arch, elevating the chin helps in providing a clear line of sight and access to the upper teeth, which are set higher in the oral cavity compared to the lower arch. This chin positioning facilitates optimal angling and maneuverability for dental instruments, ensuring comprehensive polishing while maintaining patient comfort and safety.