Math Portfolio: Fishing Rod

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  Ismar Hota

Math Portfolio: Fishing Rod

The table shown below shows the distance for each of the line guides from the tip of the fishing rod.

The information in the above table can be presented on a XY graph; where guide number is shown on X axis and the distance from the tip is shown on the Y axis. (See graph below)

From this graph one can come to a conclusion that the points represent a part of a quadratic function. A matrix method (  ) will be used to define parameters of the quadratic function (  ) using a given points (table above).

The matrix method:

Points: (1,10); (2,23); (3,38)

a + b + c = 10

4a + 2b + c = 23

9a + 3b + c = 38

         => 

From matrix result it follows:

a = 1

b = 10

c = -1

When plugged back to the , the result is quadratic function

  

From the graph it is visible that the first five points fits the quadratic function exactly however afterwards the points don’t correspond the curve. This could be proved by calculating points from the function (see table below)

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Using graphing software the lack of correspondence to the curve can be narrowed (see graph below).

From the graph it is visible that all the points almost fit the function exactly. However the lack of correspondence is very limited but not a single point fits the curve exactly whereas the first equation that was found using matrix method fits the first five points perfectly. This is proved by calculating points from the function (see table below)

This allows for a conclusion to be made that the function better fits the model ...

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