Final answer:
The most important laboratory test to check in a patient with purpura is coagulation studies.
Step-by-step explanation:
The laboratory test that would be most important to check in a patient admitted to the acute care facility with purpura is Coagulation studies. Coagulation studies, also known as clotting studies, assess the blood's ability to form clots. Purpura is a condition characterized by bleeding into the skin, mucous membranes, or internal organs, which suggests a potential problem with blood clotting.