Yea, that's right. Algebra II for most of you. If you did this in Algebra I, I am jealous of you. I learned to complete the square in Algebra II. It was a fun class for me with most of my friends from school. We tended to move from class to class together.
I was the slacker of the group, they were all in the top 10 of the class (of 559) I was just in the top 10%, but I was top dog in math. I was not the kid that reminded the teacher to assign homework, because I didn't do any until my senior year... wow, did that make a difference in my grades. But I digress.
There are a lot of good teaching and learning diaries here on Dkos (plf515 and algebrateacher are among the many many many good ones). I have a lot of interests, but math and physics are very near the top of the list (electing MORE and BETTER democrats is right up there, Civil rights is probably the top of the list.) If you can stand my momentary digressions, follow me below the fold...
It was a Friday afternoon and we were taking our test on "Completing the Square". There was a fifteen (15) point bonus question. Using the equation Ax^2 + Bx + C = 0, complete the square and simplify.
One thing I have never understood about some students, is their complete disregard of bonus questions. They just won't do them. I am talking about students that will Ace an exam, but not attempt the bonus question. Like, somehow, it was cheating. I am not one of those students. I do the bonus questions. It is an extra chance to score more points... "No thank you, sir, 100 available points is enough. I won't bother with the bonus". GRRRR. But not me. I wanted Every Point. It was a game of wits with a Sicilian with "death on the line".
Anyway... I completed the "regular portion" of the exam and set on the bonus question. Ax^2 + Bx + C = 0. Complete the square. Was this a trick of some sort? What the hay, just plow forward. I did and ended up with a miracle. I had arrived at x = [-B +/- Sqrt(B^2 - 4AC)]/2A.
I left the class with a cheese eating grin... I was onto something. I started making up quadratics and solving them without factoring, graphing or completing the square. I just plugged in A,B,and C. That weekend I figured out that if B^2 - 4AC is a perfect square, then the quadratic factors. I figured out that if B^2 - 4AC = 0, then the quadratic itself was a square. That weekend I figured out that if B^2 - 4AC <0, then there were no x-intercepts. It was a wondrous weekend of discovery. I had a secret formula for quadratics. I could even discriminate between types of solutions: Rational, Irrational, not Real... I was the King of Math.</p>
I came to class on Monday afternoon and I was a super-hero. I had conquered the quadratic equation. HEHEHEHE, I just plug in A,B and C and VIOLA! (sic) I had the answer. I sat at my desk with even a bigger Cheese Eating Grin than I had left with on Friday. That is until.... glup, the teacher wrote on the board, in big letters, underlined... THE QUADRATIC FORMULA.
Thus by striving to learn are all men made equal.