Final answer:
The inferior alveolar nerve is anesthetized to block pain in the mandibular teeth of one quadrant, by administering anesthetic before the nerve enters the mandibular foramen.
Step-by-step explanation:
The nerve that is anesthetized to block all pain sensation for the mandibular teeth in one quadrant is the inferior alveolar nerve. This nerve enters the mandibular foramen and runs down the length of the mandibular body in a tunnel, supplying the lower teeth with sensory information. To achieve numbness in dental procedures, a dentist administers an anesthetic into the lateral wall of the oral cavity before this sensory nerve enters the mandibular foramen.