Parabolas and Water Fountains

The term parabola is often associated with the quadratic equation but students often encounter parabolas much earlier in their studies. For many, a parabola is simply a “u” or an “n” shape; either the top half of a circle or the bottom half. Later, when students start transforming the graphs of functions they begin to notice that parabolas can be wide or narrow in addition to being the shape of a “u” or an “n”. It was Apollonius who gave the shape its name, but it was Galileo who showed that projectiles falling under uniform gravity follow parabolic paths.
We can find parabolas everywhere in nature including water fountains.

What better way to introduce parabolas to your students than to take them to the local park and view the water fountains (If travel is an obstacle, look to your hallway to investigate the drinking fountains).

Potential questions to ask your students:
-Is the shape positive or negative?

-Is it narrow or wider than the graph of x^2

-Where is the vertex?

-Where on the graph is its slope zero?

-Where on the graph is its slope positive?

-Where on the graph is its slope negative?


Extra credit type of questions:

-What is a way to determine the area under the parabola?

-Given two parabolas and two potential equations, which equation is probably the best fit for which graph?


More involved experiment:

-Have your students use yard sticks for your x and y axis and try to find the equation of the parabola.