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#1 2011-09-28 23:45:33

From: Bumpkinland
Registered: 2009-04-12
Posts: 105,355

Interesting maximum problem


This came up in another thread. … 34#p191934

We need to find the coordinates of M when BA is a maximum. Geogebra to the rescue!

1)The equation of the parabola can be determined by symmetry. It is:

2) Enter into the input bar f(x) = -2*x^2 - 4*x and press enter.

3) Enter into the input bar g(x) = x+2 and press enter.

4) Create and label 3 points O(0,0), C(-1,2), D(-2,0).

5) Pick a point that is on the left of C and place it on the parabola. Label it B.

6) Now drop a perpendicular line from B to the x axis.

7) Find the intersection point between this perpendicular line from B to the line x+2. Call this point of intersection A. ( use the intersection tool ).

8) Use the distance tool to measure the distance from B to A. It will appear in the algebra pane as distanceBA = something.

9) Set rounding to 10 digits.

10) use the move tool to slide point B along the parabola. See how close you can come to 1.125, I got 1.1249967. That is the maximum length of BA.

11) Go into the algebra pane and find x = -1.24941724. That is the x coordinate you seek.

View Image: mine.png

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.


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