Whats the best way to approach a teacher when they are flat out wrong and have graded you negatively, and you want to get the grade reversed?

Approach the teacher calmly and explain that you do not understand why they have marked your answer as wrong. More often than not when they explain the process of getting the correct answer, they tend to realise they got it wrong and not you. If this is not the case and they still believe they are right, explain how you got your answer and then they tend to understand. If this does not work, try and find a reliable source that suggests you have the right answer. Perhaps your teacher marked someone else's question right who wrote the same answer as you. Look through your revision material and helpful books. But just make sure you can explain confidently how you got your answer.