- Kevin Bao

# Learning Quadratics

By Kevin Bao

One Christmas break in my 12 year life-span I was learning how to expand and factor things like (a+b)^2 = a^2 + 2ab + b^2. This was completely new to me and it was my first time experiencing how difficult it was to understand concepts in math. All of the expansions and factoring tricks needed to be memorized, and it took forever, so I was still struggling. However, three days later I was like a magician at it. After I understood it I got introduced to quadratics which was also a completely new thing I had never learned before. With the help of special factorizations I was able to understand most of quadratics, but there was still something that I had not been introduced to: the quadratic formula. This formula looked complicated but I got the hang of it in a few hours. This was a huge success. I did not realize how important this was until this day. But when I used it in problems I had a really hard time factoring equations into the correct form. This turned out to be a problem because factoring is the most important part of quadratics and I was really bad at it. I spent the next week learning ways to factor like completing the square or getting rid of the coefficient. After this week I tried to do these problems again. I did problems 14.1, 14.2, 14.3 and 14.4 very easily but I struggled on 14.5. This made me face a whole new challenge. This problem included expanding and a whole lot of other mathematical concepts that I learned before. This problem really tested me. Added on to that, there were fifty more problems in the review section that I was doing. I was screwed. I knew if I could do half of them I would be good to go on. I spent the next 2 weeks working on quadratics. Then I tried it again. It was better than the last time I tried it but I got stumped on 14.16. The problem was part of the challenge problems in that chapter. The challenge problems were making my life only more painful than it already is. I spent the next week using up all my time just trying to give myself a chance at mastering this chapter. At this point I was really (really,really,really,really,really) bored on this topic. Little did I know this effort that I put in would pay off for a while. I gave my last shot at doing 14.25 and I was in shock when I saw the result. I had done it with about 100 hours of plain grinding. I had done it! I had faith in myself. The next few chapters were basically on graphing quadratics and quadratic inequalities. This made life a lot easier knowing what basic quadratics and all those factoring and expanding tricks