"The student and I went over the material his teacher went over with the class over the past week, including: quadratics, and the differences between standard, vertex, and factored form of functions. Quadratic polynomial functions will be a central focus in the coming weeks, and it already seems his teacher has started them on some problem associated with quadratics.
He is a bright kid, and his problem is not with respect to the principles associated with these topics. I think what he should focus on are problems which incorporate a number of different principles. Basic ideas concerning numbers, equations, or graphs may seem easy for students at first, especially when going through homework problems. But too often are homework problems given by teachers rested on just one principle. I think the student should practice more, but not completely, on multifaceted problems; perhaps problems with multiple parts or problems incorporating a number of tools.
I left him with a sheet highlighting some main principles, and a practice problem in which he is given three points and he must find the quadratic function on which those points lie using a system of equations; systems of equations and indeed this type of problem are things we went over during the last half of our session. I think we should continue going over quadratics and different properties and utilizations associated with them. Quadratics are popular and quite useful topics of conversation in the field of algebra, and if he continues to pursue science or mathematics beyond high school this is something he should have ingrained.
The few topics concerning quadratics they went over in class, I felt the student was coming to an understanding of them more easily than I anticipated. They focused especially correlating functions in standard, factored, and vertex forms with their respective graphs; a big focus of this section seemed visual, which is what we stuck with for at least the first half of our session. He had mentioned during our first session he was more of a visual person; it showed."