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Monday, September 19, 2005

I`m not very good at this but ill try my best.
uhm,okay ...
So we started class by talking about the on-going project. It`s about making that class character or something that will have a problem and we have to use math to solve it. OR picking any topic that we've learned and make a video about it.

And we learned more about "Completing the Squares". If a is > than one then you can factor it out first. For example:

y=2x2-12x+13
=2(x2-6x+9-9)+13
=2[(x-3)2-9]+13
=2(x-3)2-18+13
=2(x-3)2-5

the 2 is outside the bracket because it is more than 1. and if you`re wondering how we got what's inside the round bracket... this is how,first you take half of the middle term then you square it. (x2-6x+9) = (x-3)2. After that we distibute 2 to whatevers inside the square bracket and thats how we got y=2(x-3)2-18 then bring down the +13 and the answer will be y=2(x-3)2-5.

look at the example that i just made... is that how you did your work? is that how you wrote it? if that's how you wrote it then you just lost some marks. why? because the "y" or "0" is not written before the equal sign. Remember what Mr. K said... DO NOT FORGET TO WRITE DOWN THE "Y" OR ZERO. so it should look like this...

y=2x2-12x+13
y=2(x2-6x+9-9)+13
y=2[(x-3)2-9]+13
y=2(x-3)2-18+13
y=2(x-3)2-5

We also learned how to find the roots.
But first, how do you know if it has roots?

f(x)=a(x-h)2+k

we only need to look at the a & k.
if the a > 0, the parabola opens up and if the k > 0 then it wouldnt have roots because it is above the x and it opens up. but if a is greater than (<)0 and k > 0 it has roots because the parabola opens down and the k is above the x.

finding the roots or x-intercepts.

how do we find the roots of y=(x+3)2-16?
first we just balance the equation.

0 =(x+3)2-16
let y= 0
16=(x+3)2
move the 16 to the other side of the equal sign
-3+4= x OR -3-4=x
take the square root of both sides
-3+4=1 and -3-4=-7
so therefore: x=1,-7
*note: dont forget to write the "x=".

okay so that was easy... but what if its not a perfect square?
it doesnt matter if it is or not... it still has roots.
example:


-let y=0
-then move 5 to the other side of the equal sign
-then take the square root of both sides.
- move the 3 to the other side. (it becomes negative)

^^ and you can leave the answer like that.




important things to remember:
-DO NOT DROP ONE SIDE OF THE EQUATION or FORGET TO WRITE THE "Y"/ZERO because if you do, you`ll end up losing marks.
-always write "x=" when writing the roots/x-intercepts.
-some equations are prime but still has roots.
-when drawing a graph don`t forget to label them.. it`ll also cost you a mark.

*i know these things were said million times already but ya... just a reminder ;) * hehe

well... thats all i could remember for now. til next time! ^_^



AND TOMORROWS SCRIBE IS... Robert.



4 Comments:

At 9/19/2005 8:51 PM, Blogger AichelleS. said...

insane blog...it's so good

 
At 9/19/2005 8:52 PM, Blogger Richy said...

Wow... Just wow... Excellent Scribe post.

 
At 9/19/2005 9:26 PM, Blogger Abdi said...

i think you are good at this cuz thats a pretty long explanation.
anyways good job.

 
At 9/19/2005 9:56 PM, Blogger Mr. Kuropatwa said...

Kat, I am in awe .... you've taken this to a completely new level! I loved your use of colour. This post will be tough to beat.

There are a couple of small technical things I'd like to clear up though:

(1) In the "coloured" section you've got a line that contains a <> k > 0. This is a little confusing to me.

(2) The phrase take the square root of both sides should be moved up one line and the equation should show the result of doing this.

The graphic is awesome! Really, you've far surpassed any expectaions I had. Bravo!!

 

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