Is there a method for notifying the teacher that the student has completed a quiz based on reaching a specific grade or above a specified grade?
We have a faculty who wants to be notified only when a student has reached a specific grade or above for a quiz. There no method in the course shell for the faculty to use a specified grade to send a notification email or message. Reviewing if this is possible through an API call.
There isn't a single API call that would enable this.
But you could schedule a program that would retrieve the quiz grades via the API and email the faculty when the necessary conditions were met.
You can actually subscribe to all of the Quiz_Submitted events via web hooks. There is some documentation over here to help you answer your own questions.
This wouldn't have all of the info (as in what grade they need to get above) but it would be a start.
You may want to read through https://community.canvaslms.com/thread/22324-copying-notification-emails-to-faculty as it seems to be somewhat similar in nature to your own question.