To start class, we went over the quiz we took Wednesday. Number four was found to have a cost of zero when x=80. Therefore, Mr. O'Brien gave the option of making a note on this problem if we got it wrong for this reason, and passing it back in. We then switched gears, and looked at the projects done by our classmates. We then went over the previous night's homework, involving imaginaries. Mr. O'Brien pointed out that with imaginaries there are often multiple ways to solve the problem. This discussion lead us to the fundamental theorum of algebra. Counting multiplicity, every nth degree polynomial has n complex zeros. We were then introduced to the rational roots test. This states: If a polynomial function has rational zeros, then they must be of the for a/b, where a is a factor of the constant term and b is a factor of the leading coefficient.

Friday, October 23rd

We warmed up with two simple questions, one from the book and one that Mr. O’brien came up with. The problem from the book was number 42, a cubic function with three different roots. The other one was a quartic function, and we were able to solve it through the use of Wolfram alpha, or guess and check, but lead to our later exploration of Polynomial Long Division and Synthetic Division later in the class.
Before we refreshed on these two forms of division, we went over homework, which was composed of problems from section 2.1 and 2.2. since this was our first time looking over chapter two homework together, we refreshed on some basics, like finding the Axis of Symmetry (of quadratics) and and the roots of polynomial functions etc. This will be the material present on next class’ quiz.
Our lesson regarding Synthetic Division and Polynomial Long Division showed us that while both were effective, each had their time and place. Synthetic Division was more simple, but Polynomial Long division could be used regardless of what the polynomial is being divided by. We then saw how the remainder theorem can help one find function values.

Scribe Post 10/27/09

At the start of class we had a quiz on the 2.1-2.2 homework. This took us up to 10:05, and from there we began going over some of the more recent homework problems, including pg. 159 (13, 23, 49, 25, 59, and 37). Problem 37 segued nicely into a discussion of the remainder theorem, which as we learned can be used to quickly find specific values of a function such as f(5). Next, we did a review of complex numbers, proceeding with a Venn-diagram of the various types of numbers and the relationships between them. This lead discussion towards terms such as rational, irrational, pure imaginary, etc.; we also reviewed operations involving complex numbers, including a brief discourse on complex conjugates. This took us right up to 10:50, our homework being p. 167/17, 19, 21, 29, 33, 37-51 odd, 65, 71. I haven't gotten a chance to talk to anyone about being the next scribe yet, so I'll do that at the beginning of next class.

Homework for 10/27/09

I was unclear on how to do pg. 159(37). Could we go over this in class? Thanks!

- Molly W.
W-2 Pre-AP Calc

HWK assigned10/18

I had trouble on problems p.134/23 ,79, p.149/21, 29, 33, 41. I forgot how to put parabolas in standard form and also forgot what a and b are in the equation for the axis of symmetry.
-Henry W-2

Pre-AP Calc 10/19/09

Class summary and notes!

The first 2o (it was ACTUALLY 25) minutes of class we spent taking the Suppercorrection quiz. Then we worked in our books on page 134, going over a matching-function-to-equation exercise. We saw the definition of polynomial function, which we won't need to learn, phew (it's REALLY complicated-looking). Then we went on to learning about polynomial functions. WolframAlpha!

•Linear functions are a special type of polynomial functions

•Every polynomial function has the property that they always are ARN

•As x approaches infinity, the function itself also approaches infinity

•As x approaches -infinity, the function also approaches -infinity.

•An odd degree means that the end lines go in opposite directions.

•An even amount of turning points means the end lines go in opposite directions.

•The amount of turning points is AT MOST one less than the exponent.

•Double roots (or roots with multiplicity).

•Even routes make a smooch.