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#1 2012-04-18 07:10:23

From: Bumpkinland
Registered: 2009-04-12
Posts: 86,219


This problem popped up in another thread and can be solved by standard methods.

For the curve  y=x^2+5x
a) find the gradient of the chord PQ where P is the point (2.14) and Q is the point (2+h,(2+h)^2+5(2+h))

Let's see what geogebra can do.

1) Draw the curve by entering f(x) = x^2 + 5x.

2) Enter the point (2,14). Call it P.

3) Create a slider called h. Range it from -5 to 5.

4) Create a new point ( 2+ h, h^2 + 9h +14 ). Call it Q.

5) Draw a line between P and Q. Get the slope m of that line using the slope tool.

6) Slide h back and forth and notice the value of m in the algebra pane.

7) Record those values like this:

8) Conjecture the obvious relationship of m = h + 9.

Your geogebra worksheet should look something like this.

View Image: 2012-04-19_002922.gif

In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.


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