Ben Cosh

George Reuter

IB Math

20 January 2013

Gold Medal Heights

Introduction: a) The Olympic Games is an international event featuring summer and winter sports, in which athletes participate in different competitions. Since the Olympic Games began they have been the competition grounds for the world’s greatest athletes. First place obtaining gold; second silver and third bronze. The Olympic medals represent the hardship of what the competitors of the Olympics have done in order to obtain the medal. Olympic medals could be used as a unit of measure of athleticism.

Data Provided:

[pic]

Height (in centimeters) achieved by the gold medalist at various Olympic games.

The following is a graphic representation of the
*…show more content…*

When using this linear function, we can see that the function is somewhat accurate for the years 1956-1972. Unfortunately in other years, the linear function is not a good representation. Because of these differences, the linear equation found is not a perfect representation of the given data.

Developing a Function with Technology:

After further examination, a new function must be formed to better fit the data given. This function which I now believe fits the data well is the quadratic function. I believe that the quadratic is a good fit because the data seems to take the same shape as a quadratic, x and y values both rise in a gradual way.

The general quadratic function is as follows:

Using technology we can find the values of all variables: “a”, “b”, and “c”

Technology has found the following variable values.

A=

B=

C=

These values result in the following quadratic equation;

The following is a graphic representation of the new function found and the given data. The new function found is much more accurate when comparing to the linear function found earlier.

The following table holds the values of the given data and the values found using the quadratic function found earlier.

[pic]

This is the best fit because as we can see from the graph it fits most points

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