Fishing Rods Portfolio. Leo has a fishing rod with an overall length of 230 cm. The diagram shows a fishing rod with eight guides, plus a guide at the tip of the rod.

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FISHING RODS

A fishing rod requires guides for the line so that it does not tangle and so that the line casts easily and efficiently. In this task, you will develop a mathematical model for the placement of line guides on a fishing rod.

Leo has a fishing rod with an overall length of 230 cm. The diagram shows a fishing rod with eight guides, plus a guide at the tip of the rod.

The table below shown below gives the distances for each of the line guides from the tip of his fishing rod.


The distance of each guide from the tip of the fishing rod is measured in cm. The
x value, or the independent variable, is the guide number, and the y value, or the dependent variable, is the distance from tip. Only positive numbers can fit this scenario, because a fishing rod cannot have negative lengths. We can even further limit the domain, because the fishing rod only has 8 guides, so x would have to be greater than or equal to 1 and less than or equal to 8.

The graph of the data would look like this:

Quadratic Function: (ax2+bx+c)

To find a quadratic function for this data, I used the first three guide numbers and distances from the tip: (1, 10), (2, 23), (3, 38) and used these numbers in the matrix method

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To find [X], we could use this formula:

Quadratic function is:

Cubic Function: ax3+bx2+cx+d

The same method was used to find the cubic formula, except that the first 4 guide numbers and distances were used in the matrix method. (1, 10), (2, 23), (3, 38), (4, 55)









To find [X], we could use this formula:

So:

So, the Cubic Function is:

In order to graph accurately, I decided to only graph the quadratic and cubic functions only with the domain of the original data points. This domain ...

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