ask for forgiveness, not permission.
i'm kidding i'm kidding. don't do that or that won't trust you. present your stance respectfully and calmly. tell them why you want a pixie cut, how it'll benefit you (like, i don't know, self expression?), and how you think you're mature enough to make your own decisions regarding your appearance. all of that stuff that parents always want to know. maybe think of some counterarguments. like, what would they say if they argue, "it won't make you look good"? maybe you'd say, "i think it would look good, and even if it doesn't, it's just hair and it'll grow back." don't get angry, don't whine, and be mature about it so that they know they can take you seriously.