This is the chapter on Root Finding Algorithms from a larger project I wrote: A Numerical Methods Companion for High School Mathematics, which intended to be an aid for teachers of 10th, 11th, and 12th grade math to introduce computer science concepts in a manner which parallels topics taught in a standard math curriculum. Included in this PDF is a chapter giving explanations for many root finding algorithms, including Bisection Method, Newton Method, and Secant Method, along with worked out exa