No, in proper punctuation and grammar, a quotation should always have both a starting and ending quotation mark. It would not be correct to only have an ending quotation mark without a starting one.
I said that both quotation marks are needed, and my teacher gave me an F grade
I apologize for the confusion. If your teacher specifically marked you down for including both quotation marks in a quote, it may be worth discussing the specific guidelines with them to better understand their reasoning. In traditional grammar rules, both a starting and ending quotation mark are typically required. It's possible that your teacher has a specific style guide or preference that differs from traditional rules.
