sometimes only half of a parabola is used to model data. Why is this the case? Why would we not be interested in both sides?

Question

Sometimes only half of a parabola is used to model data. Why is this the case? Why would we not be interested in both sides?

Answer 1

A high diver jumps off a 10 meter platform, model his height above the water at any time after he jumps.

 

If y is the height above the water, g = -9.8 m/s^2 is the acceleration due to gravity, and x is the time in seconds after the jump, then:

 

y = -9.8x^2/2 + 10.

 

That's the equation of a parabola with vertex (0,10) and opening downward. But the real domain is x ≥ 0 seconds; i.e., the right half of the parabola.

 

Here's a fun video: go to http://www.learner.org/resources/series42.html?pop=yes&pid=549#program_descriptions, click the VOD badge to the right of "2. The Law of Falling Bodies" and watch from position 10:20 and following. The first 10 minutes is interesting too, if you want to go back and see it from the beginning.

Answer 2

Hi Ness;

It is possible we only need positive values of x.