Final answer:
A 'writ of certiorari' is the document that requests the Supreme Court to review a case and also doubles as a brief. At least four Supreme Court Justices must agree to grant the writ for a case to be heard.
Step-by-step explanation:
The written document that asks the Supreme Court to take a case and also serves as a brief is known as a writ of certiorari. This writ is a request for judicial review, seeking an order directing the lower court to send its records to the Supreme Court for review. A petitioner files for a writ of certiorari, and if granted, the case is scheduled on the Court's docket.
The granting of certiorari is dependent on the 'Rule of Four,' where at least four of the nine Justices must vote to accept the case. The Supreme Court typically exercises its discretion to hear cases that present a constitutional question or where there is a significant legal question arising from differing interpretations of a law by various courts.