## Saturday, June 4, 2011

### 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).

-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.

Harry said...

Hi,

Nice fountains, these are specially for summer season. People are getting cool with bathing with friends. Government now tries to provide more fountains in public place like hospital and hotel for relaxing. Thanks a lot.

Scale In Water

vijay shukla said...

Excellent overview, it pointed me out something I didn’t realize before. I should encourage for your wonderful work. I am hoping the same best work from you in the future as well. Thank you for sharing this information with us.

Jeremiah Dyke said...

Thanks for the feedback everyone!

Anonymous said...

Fountains are so interesting, here I am, worrying about parabolas, when I could be looking at relaxing fountains. Thanks a bunch buddy!