"We started our session with graphing parabolas. We talked about the two methods for finding the vertex of a parabola (completing the square or using the formula). We then talked about how to find the x and y intercepts and use them with the vertex to graph the parabola by hand. Initially, the student was confused about how to know if the parabola will be concave up or concave down, so I explained that when the formula is in the form of ax^2+bx+c then if a is negative, the graph will be concave down and if a is positive, it will be concave up. We also talked about the standard form of an equation for a parabola and how to find the vertex from that. We then applied this concept to word problems such as finding the max revenue or profit when given an equation that yields a parabola. The student overall did well with this concept and seemed to follow it easily. Next, we talked about quadratic inequalities and how to find the set of solutions for a quadratic inequality. The way that the book presented these problems was a bit confusing for the student, so I taught him how to approach the problems a different way and then, once he understood that, we went back and used the technique in the book. He seems to have a good start on understanding this material, which is good since they haven't even started it in class yet. Lastly, we reviewed the two practice sets from the grammar packet that he was supposed to do for homework (on verb agreement and comparisons). We reviewed how to solve these kinds of problems, and he quickly remembered and got the problems right. Next, we talked about correct usage (no double negatives, no redundancies, etc.) and reviewed the first practice set. We also talked about the correct rules for capitalization and practiced with the first practice set. The student will do both second practice sets as homework for next time."