This is a blog for my second semester pre-calculus 30s students. Have a blast!

Wednesday, February 15, 2006

Scribe Post #2

Well hello everyone.. I'm Tim-Math-y your scribe for today. I'm going to try and do this quick so everyone can read it and so that it won't take up too much of my time.

Today, we started off class with Mental Math which included 11 questions. Next we did a 10-15 minute review of last night's homework: Ex. 3 (questions 5a, 5b, 7, 8, 4c, and 11).

Now onto today's lesson!

TRANSFORMING GENERAL TO STANDARD FORM

*This proccess is referred to: completing the square.

When thinking about this, we think back upon "Alge-tiles".

---Sigh.. unfortunately, it says error when I try to add images.. so please bear with me on this Scribe post holding no visual pieces... (-.- )---

y = ax2 + bx + c ---> General / Expanded Form

>>>Consider:
- a square with length of (x+1) and a width of (x+1)
- the area would be expressed as (x+1)(x+1) --> x^2 + 2x + 1

>>>Consider:
- x^2 + 2x + _?_
- to complete the square, the unknown is equal to 1.

>>>Consider:
- x^2 + 4x + _?_
- to complete the square, the unknown is equal to 4.

Do you see how to find the unknown value of C by looking at what's givin?

*In a quadratic func in general form:
C = (b/2)^2 ... is used to complete the square

>>>a perfect square trinomial is where a trinomial has 2 equal factors.

Example: x^2 + 6x + 9 = (x + 3)^2
Example: x^2 + 8x + 16 = (x + 4)^2

>>>convert from general form ----> standard form by completing the square.

Example:
y = x^2 + 4x - 5
Step (1.) y + 5 = x^2 + 4x
Step (2.) y + 5 + 4 = x^2 + 4x + 4
Step (3.) y + 9 = (x + 2)^2
Step (4.) y = (x + 2)^2 -9
V = (-2, -9)

Example:
y = 3x^2 - 12x + 16
y - 16 = 3x^2 - 12x
y - 4 = 3(x^2 - 4x)
y - 4 = 3(x^2 - 4x + 4)
y = 3(x - 2)^2 + 4
V = (2, 4)

Now that those two are done, Mr. Malandrakis decides to blow our minds with the so called "friendly" fractions..

Example:
y = -2x^2 - 5x + 3
y - 3 = -2x^2 - 5x
y - 3 = -2(x^2 + 5/2 x)
y - 3 - 50/16 = -2(x^2 + 5/2 x + 25/16)
y - 98/16 = -2(x + 5/4 )^2
y = -2(x + 5/4)^2 + 49/8
V = (-5/4, 49/8)

__________ / / __________

*In any quadratic function in standard form:
h = -b/2a
K = 4ac - b^2/ 4a

Example:
y = x^2 + 4x - 5

h = -4/2
h = -2

K = (-2)2 + 4(-2) - 5
K = 4 + 8 - 5
K = -9

V = (-2, -9)

And that is all folks! Wow.. I can smell dinner from downstairs.. I'm sure HUNGARY :). But before I am done, have to mention some things ^^.

Mr. Malandrakis: "It is very important to take some time to read what's on the blog."
Tomorrow's Scribe: (sorry no drum roll :P) It is.. MR. "StevenF" because he said it's fine by him ^.-
Homework!: (which is essential for this course) EXERCISE #5

And for sure now, I think that is all.. see you guy tomorrow! I'm going to eat dinner :P






17 Comments:

Blogger John D. - #12 said...

This comment has been removed by a blog administrator.

6:34 PM

 
Blogger John D. - #12 said...

This comment has been removed by a blog administrator.

6:35 PM

 
Blogger John D. - #12 said...

Marvelous post! Although there are some errors.


y = ax + bx + c ---> General / Expanded Form

should be:
y = ax^2 + bx + c - you might want to correct that.

You might want to use the superscript tag: (sup)(/sup)(*note: replace the () with <> because Blogger doesn't want HTML tags on the comments.) so that you don't have to go the old fashioned way of using ^ to indicate a power. For all those who want to use Blogger to its fullest potential, go to this
Click the link on that post.

Otherwise, great use of colours, although you might want to use different varieties. Great scribe post.

Cheers!

6:36 PM

 
Blogger Jamie G. said...

Good job tim-Math-y! Your post really helped me to catch up on what i missed for this day. At lease I have some idea now of what you guys have done in class today! (you might want to use different colors next time, and avoid using black because it's too hard to read when the background color is dark). However-it was a GREAT POST(Y)

6:47 PM

 
Blogger tim-Math-y said...

lol ok mr john. pfft what a commenter -.-, i will go fix it. also, if the black or any color is bothering you, you should view the posts in iblogger when you log in. truthfully i dont like the dark colored background of the actual blog.

Oh and i like to keep things simple, the old fashioned way ^^

6:55 PM

 
Blogger Richy said...

Hey Tim-math-y. Richy here. Read the Scribe. All I can say is... Very Imaginative Title. Hahahaha. But for real this time... Excellent work on the scribe post. I like how you started with a paragraph and ended with some random parts of the class. Hahaha. Typical Steven. Hahaha. Nice one Timmy. Oh yeah. About the image thing. Try changing your format to a Jpeg or a Gif. For my computer Blogger Doesn't like Bitmap's. Ok that’s all from me. Later.

9:05 PM

 
Blogger Mr. Malandrakis said...

Tim,

This is a fantastic post. You and John have definitely set the standard so far for what great students are. Keep up the excellent work!!!!

Nick

1:02 AM

 
Blogger tim-Math-y said...

thanks guys lol, this comment is little late :D, but i gtg do hw

9:20 PM

 
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