8. The water fountain

The photograph shows water squirting from a drinking fountain. Your task is to use your knowledge of graphs to find a function y = f(x) that models the curve formed by the squirting water.

If you click on the photograph, the coordinates of the point are shown at the bottom. You can fine-tune the selected point by clicking on the blue arrows - each click moves the cross hairs one pixel in the chosen direction. This is the same applet you used in “Battlefields” in Unit 18.

So you must gather data from the picture, then use this data to find an algebraic formula modelling the curve.
If you want to use regression methods to find the best fit, you can use this Excel Worksheet as tool if you prefer. But make sure that you can also find the formula using algebraic methods!

After finding your formula, you can check it by entering it in the above applet. To specify the function, you must:

• give the domain of the function (enter the smallest and the largest value of x), and
• give the formula of the function (enter your values for a, b and c, or type in your own formula, but note the computer notation *, ^, etc.).

Then click the "Check your model" button. A new window will open, showing your graph on top of the photograph and you can judge how good a fit it is …

Reflect on your solution strategies ...
What are the important mathematical ideas that you have used?

Source:
Adapted from Journal of Online Mathematics and its Applications
This is an external link.