A petition for a writ of certiorari. If the Supreme Court agrees to hear the case, they grant cert(iorari); otherwise, they issue an order declare cert(iorari) denied. After the Court accepts a case, it issues a writ of certiorari to the last court to handle the case, ordering the relevant files be sent to the Supreme Court. The case itself is said to be "on certiorari from [name of lower court]" (e.g., On certiorari from the US Court of Appeals for the Fourth Circuit).
For more information, see Related Questions, below.
If the US Supreme Court is the first to hear a case, the Court has original jurisdiction.
In the Supreme Court, the written decision and legal reasoning for a case is called an Opinion.
No it was not a supreme court case, but a state case because it was held in the local court
When the US Supreme Court agrees to hear a case, it issues a legal order called a "writ of certiorari" telling the lower court to send up the case files.
case files
Centarori
The Supreme Court referred to slaves as property in the infamous Dred Scott v. Sandford case of 1857.
Centarori
Writ of Certiorari
When the Supreme Court is the first court to hear a case (which is very rare) it is said to have "original jurisdiction." What I think you meant was, when the Supreme Court considers an issue it has not thought about before, it is called "a matter of first impression."
The written explanation for the US Supreme Court's decision is called an opinion.See Related Questions for an expanded explanation.
A case on appeal reaches the supreme court if the judges below them cant handle it or that case specifically but it is very hard to get a case on appeal in the supreme court