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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,237

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

**For the curve y=x^2+5xa) 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.

**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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