Newton's Method is a straighforward, user-friendly means to find zeros of functions. It works iteratively – you take an initial guess, apply a simple procedure to improve that guess, and then repeatedly feed the result back in. Newton's Method is robust (it very rarely fails to find an answer) and fast (its answer approaches the root in very few steps). It also leads to some surprisingly beautiful mathematics and helps illuminate a perplexing “feature” (bug) of most graphing calculators. These important and interesting topics are all accessible to advanced high school students with basic calculus.