1. Ask
2. Tell them the truth and present your parents with valid reasons why you should or need to be homeschool over public schools.
3. Why?
How can i convince my parents to let me be in home school?
One of the biggest things I think a parent is afraid of when it comes to home schooling their child is "will I be able to get them to do their school work?" "Will it be more of a chore then a joy?" Etc. Be sure to SHOW them that you are doing your homework right now WITHOUT them even telling you to. Might help. Good luck. :0)
Your parents would want your good. Make sure you already know about the cons and pros. Sometimes you might seem certain about a purpose you have. But the fact is you know nothing but your parents been there and seen more than you ever can count. So you might want to listen to them more responsibly and effectively but in return, ask them to listen to you then.
Gather articles and information regarded the cons and pros of each major. Provide it to your parents and let them observe and give out the outcome.
Explain your comfort zone and will widely and reasonably.
Make them see how certain you are about your choice, assure them you have the details under control and you know what you really doing with your life. Make them feel that you are making this decision with full acknowledgement.
If you're under 18, make sure you know how to tone up your voice, being rude, reckless and loud won't help you. Being reasonable, calm and responsible is the key. Request, don't order. Discuss, don't argue. Relax, don't fight. Act mature, don't be immature. Then you might have chances.
Since we don't know your situation, there isn't really much we can do to help. Do you have a valid reason for this request? Is there someone who is going to be home to supervise your schooling? You have to look at what it will involve for that to happen and how it will effect your family. It can't be just because you want it.