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Wednesday, September 14, 2005

Scribe THIS!

Well today's class went pretty well if you ask me. First started off with a few review questions about interval notation, figuring out if a point is on a graph of a function and finding different parts of a parablola. The interval notation part we didn't really go through heavily for one because most of us understood how to do that so GOOD JOB GUYS! Well at least that's what it seemed like since no one had any problems on them. The only thing we went through for the interval notation was a new concept known as Union, which is when you have exceptions for which 'x' can be. Example of that would be like [-10,-2] U [2,10], and that would be read as including -10 to including -2 UNION including 2 to 10. I don't know if I explained that properly but yeah comment if its wrong and I'll edit it.

Then the point on a graph of a function we went through thoroughly because it seemed as though we didn't know how to do it or just simply forgotten about it, but as soon as Mr. K went through it, it got easier and everyone seemed to understand how to figure out if a point is on a graph of a function. Then the last question about finding parts of the parabola everyone seemed to have gotten the idea. From seeing a graph and determining its Vertex, the X-Intercepts, Domain/Range, Axis of Symmetry and the Max or Min. On about the x-intercepts NEVER!! write the x-intercepts as (from review from class) (-3,0) and (3,0), THIS COULD COST YOU MAYBE HALF MAYBE EVEN A FULL MARK!! Be sure to write the intercepts as x=-3, 3.

After all of the review questions and the look at the rule of four again, we went into our dictionaries and took down some notes on the standard form (y=a(x-h)^2+k), and what each and every one of the letters meant. From understanding what each letters represented we figured out that given a standard form of a parabola, you can find many things without the graph such as the vertex, if it opens up or down or if its wider or skinner than x^2. DON'T forget about Mr. K's warning about 'h', WATCH THE SIGN! Beacuse 'h' is written -h in standard form the sign of 'h' is always going to be opposite.

Then after all those heavy notes (one page) we had some fun with parabolas by finding different things about parabolas, where'd they be on the coordinate plane and if it has x-intercepts. After getting used to all of that Mr. K gave a little review on factoring and showing us that we could find where a parabola was and the equation for it by getting it's x-intercepts by factoring, but it was confusing VERY confusing. Honestly I didn't understand how he was doing it =S. After that whole confusing moment about finding a parabola by its x-intercepts Mr. K looked at the clock and RIIING next class.

BTW: Guess what? Pamela your up bat tomorrow!


At 9/14/2005 6:47 PM, Blogger Richy said...

Finally a new title... Hahaha. Excellent Summary. Very Detailed.

At 9/14/2005 8:47 PM, Blogger Mr. Kuropatwa said...

Outstanding summary! You have "raised the bar" for eveyone else. Great job Abriel!

At 8/08/2006 4:28 AM, Blogger Ms. Armstrong said...

Why should the x-intercepts be written in the form x=-3,3 and never in co-ordinate form?

At 8/08/2006 5:55 PM, Blogger Mr. Kuropatwa said...

There's no good reason really. It's an idisynchratic quirk of the Manitoba Pre-Cal Math Exam committee. They insist that intercepts (x and y) be written as described in the scribe post.

I think this perspective is pedagogically misguided. Here's why:

An important priniciple in mathematics pedagogy is teaching multiple representations. i.e. any function can be expressed in four different ways:

(1) symbolically (an equation; y = 2x)
(2) numerically (a table of values)
(3) graphically
(4) in words ("My pet otter eats two kilograms of fish each day.")

We have three names for the same object: root, zero, x-intercept.

"x-intercept" because that aligns with the graphical representation of a function.

"zero" because that aligns with the numeric representation of a function; the 'output' is zero at a particular 'input.'

"root" because that's the 'x-value' in the equation that leads to y = 0.

I teach all this in class but emphasize that the idiosynchratic decision of our exam committee means that students can loose a half mark if they express intercepts in any form other than symbolic. I'm not happy about it but that's the way it is here ... for now. ;-)


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