Final answer:
The presence of UMN signs like a positive Babinski sign points to a high cervical lesion between the C4 and C5 vertebrae as the likely site of spinal transection in the quadriplegic patient.
Step-by-step explanation:
The presence of symptoms such as increased muscle tone, hyperactive stretch reflexes, sustained clonus, and a positive Babinski sign all point to damage in the upper motor neurons (UMNs). Given that the patient developed quadriplegia following the accident but retained some shoulder movement, the spinal cord lesion likely involves the cervical region which innervates both the upper and lower limbs. Based on the provided information, the most likely location of the functional transection of the spinal cord would be at or above the cervical level but below the region that innervates the shoulders, suggesting a high cervical lesion possibly between the C4 and C5 vertebrae.