How can I convince my teacher to not give me a zero for using a graphing calculator on the test?

Ok so i was sitting in class taking my final exam. My teacher had told us that we could use a calculator but not a graphing calculator. I only had a graphing calculator at the time so i started to use it. (btw, there were graphing problems on the test.) at first i used the graphing calculator for multiplication only. then i came a problem that told me to graph a hyperbola. I proceeded to show all the work. the parabola looked about right, but just to make sure, i decided to graph it on my calculator (BIG mistake) after i graphed it out, i realized that my graphing calculator couldnt graph y^2=4ax functions. so it just look liked a weird graph. Realizing that my graphing calculator couldn't help me at all, i decided to move on to the next problem. then my teacher comes over and asks me why was i using a graphing calculator. she then took my test and calculator away and gave me a zero. now this was a final test so i dropped my grade severely. How do i talk to her and tell her that, although i made a really stupid mistake of using the graphing calculator in the first place, that other than multiplying and dividing, i had no other use from that calculator nor did it benefit me in any way. Is that still considered cheating if i wanted to check my work? How do i explain this to her? to sum it up, n my test, it clearly shows all the work possible in graphing that problem and it shows that i have complete understanding on how to graph, i was just making sure my graph was right. I really really need your guys help!