I'm a teacher and I use WM on regular basis. I use it mostly to make some exercises for my students (plotting graphs, checking if an equation has nice roots etc.). But WM has much greater capabilities than needed for a high school student.
I learned how to use WM in college and used it (along with Matlab) while I was studying math and computer science. But I think you don't really need a teacher to teach you how to use WM (especially if you already learned some programming) because it has extensive help which not only teaches you how to use it, but also explains many mathematical terms, concepts and formulas. Just click on Help->Documentation Center and search for anything you want to know how to use. E.g. type "equation solving" and you should get a list of all WM's functions for equation solving and if you click on one of them (e.g. Solve) you will see how to use it.
WM has grater capabilities than Wolfram Alpha but you will need some time to learn how to use it which should not be problem as I explained earlier.
If you have any other questions please don't hesitate to ask. You can also check the links below.
Yes, I'm a regular user of Wolfram Mathematica. It's capable of doing complex mathematics, and has higher abilities then that of a graphing calculator. I have used it to solve logarithmic functions, trigonometric functions, and their inverses. It also tells you domain, range, and maximum and minimum values. It's even capable of calculus, and can calculate derivatives. It is an extremely useful tool. Good luck!
How did you learn to use it?