How do I change a quiz answer and grade after the students have taken a quiz?

Some of my students have taken and submitted an exam/quiz, I wish to change a quiz answer without going in manually and updating every grade.  Is there a way to update the grades automatically just by changing the answer to the question and updating all grades? 

Yes.

1. Go to Quizzes tool.
2. In Manage Quizzes, click Grade from the context menu of the quiz you want to recalculate.
3. In the Questions tab, select the question you wish to update.
4. Once done Editing the question, you will want to update the students’ grades. In the Questions tab, toggle the Update All Attempts option.
5. In the Questions that are not in the quiz anymore section, click the question’s link.
6. In the Grading Type area, toggle Give to attempts with answer [new/additional correct answer] [value of the question] points.
7. Click Save.