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Tuesday, January 17, 2006

ESS-CRIBE

Today’s class started off with Mr. K. handing back our project evaluations. He also talked about acrostics for this unit. Yesterday we learned how to graph a polynomial function without a calculator or started to learn how and today we did some more of that.

Important stuff to know:
-The maximum number of roots a polynomial function can have is the number of the highest degree in the polynomial [ex. x²+6x+9~the maximum number of roots this equation can have is 2]
-the end behavior determines which way the arms of the function go [like in a parabola if the end behavior is positive then the arms go up but if it is negative the arms go down]
-polynomial functions are smooth and continuous-they have no jagged points
-the Fundamental Theorem of Algebra says that the number of roots a function has to have is the highest degree in the function [like x³~this has to have 3 roots]
—but not all polynomial functions have roots, they have complex/imaginary roots.

This then brought Mr. K. to talk about how we should stay in math when we go to university/college and he also talked about jobs—for more info go read his blog post:
http://pc30s.blogspot.com/2006/01/why-should-i-learn-math_17.html

After that we finished drawing the polynomial function without using a calculator that was on the board yesterday by doing this in these steps: [pictures may be blurry just click them]


We then got this sketch by plotting the roots and the y-intercept onto the grid and drawing the function’s basic shape:

After that Mr. K. put a question on the board that we had to do by ourselves which was draw f(x) = x³ + 3x² -13x – 15 without using a calculator. To figure this out you need to follow the same steps as in the question above ^. If you did then you got something like this:



The last function we had to graph without our calculator was f(x) = 2x^4 + x³ - 17x² - 16x + 12. We only got so far as to find the y-intercept [@ 12] the possible numerators [±1, ±2, ±3, ±4, ±6, ±12], the possible denominators [1, 2], the possible roots [±1, ±2, ±3, ±4, ±6, ±12, ±1/2, ±3/2], and we also did some synthetic division but we didn’t get to finish the whole thing because we ran short of time due to the bell, so Mr. K. said we will go over the question tomorrow.

Homework is Ex. 54 [1, 2, 3] & Ex. 55. [and if I made any errors or mistakes just let me know, thanks] ohhh and the scribe is:

2 Comments:

At 1/17/2006 7:30 PM, Blogger Mr. Kuropatwa said...

WOW! Just spectacular! I really liked the colour scheme of your images. And the annotations you wrote beside the equations are fantastic!

One thing though, you wrote about the "n behaviour," it's supposed to be the end behaviour.

(I have to practice enunciating [ee-nuhn-see-ate-ing] my words in class -- sorry about that.) ;-)

 
At 1/17/2006 10:00 PM, Blogger AichelleS. said...

okay I fixed it hahaha

 

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