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Monday, January 16, 2006

Scribe: Very Sorry Guys!

Okay, I know it's late, but I just got home for the first time since 8:30 this morning so please bare with me. Also to add to my frustrations Firefox is lost on my harddrive and I dont have enough time to dig it out or re-download it so I'm going to have to do this without pictures or diagrams.

So, it all started off with Mr. K. going around and handing out the "Go For Gold" assignment. Just as a reminder:
-Must get 100%; anything else is unacceptable.
-You can recieve help from anyone at any time on this assignment
-Copying other people's work is completely unacceptable

-Due Monday, January 23, 2006

Then, we had to take some notes into our dictionaries. They were:
-Remainder Theorem
-Factor Theorem
-Synthetic Division

(I will not write the notes in this post, because that's Graeme's job and I don't want to steal his chocolates!)

Following this we continued with today's concept:

GRAPHING FUNCTIONS W/O A CALCULATOR!!!
~We first learned a couple properties of the graphs of functions:
- All even exponents for the equation ( y=x^n ) look like parabolas ( U-Shaped)
- All even exponents for the equation ( y=x^n ) have 3 points in common: (-1,1); (0,0); and (1,1)
- All even exponents for the equation ( y=x^n ) have a minimum of 0 roots.
- All odd exponents for the equation ( y=x^n ) look like cubics (attétude position)
- All odd exponents for the equation ( y=x^n ) have 3 points in common: (-1,-1); (0,0); and (1,1)
- All odd exponents for the equation ( y=x^n ) have a minimum of 1 root.

*Note* The maximum number of roots that a function can have is equal to "n" in the equation ( y=x^n ).*


Finally, we briefly learned about the "Descartes Rational Root Theorem". However, I did not quite understand this so I will only provide the example we were taught and hopefully tomorrow Mr. K. will teach us some more about it.

EXAMPLE: ƒ(x) = 3x^3 - 4x^2 - 5x + 2

Possible Numerators( taken from the the positive and negative factors of the last term): ±1, ±2
Possible Denominators ( taken from the positive factors of the coefficiant of the first term): 1, 3
Possible Roots:(Hope This Works!)

1 ,-1, 1 ,-1, 2 ,-2, 2 ,-2
___ __ ___ __ ___ __ ___ __
1 , 1 , 3 , 3 , 1 , 1 , 3 , 3


Then you check by a new form of Synthetic Division:

* | 3 -4 -5 2
_____________
1 |3 -1 -6 -4 x
-1| 3 -7 2 0 √

.: 3x^3 - 4x^2 - 5x + 2 = (x+1) (3x^2 - 7x +2)


Well that about wraps it up, I'm very sorry, but I was very busy tonight and it didn't help that I've lost Firefox, so thank you for baring with me and I'll try to fix the problems right away.

Oh yeah! By the way there's a couple things (reminders) for Mr. K.
1. Tests back
2. Assignments back ( Mathland)
3. New Acrostic Words

Thank You

and the next scribe is...

Aichelle

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