Parabolas

"You’re just taking things apart, putting them back together again, taking them apart, putting them back together again. Art’s play."  - John Baldessari

 John Baldessari,  Throwing Four Balls in the Air to Get a Square

John Baldessari, Throwing Four Balls in the Air to Get a Square

In 1974, John Baldessari completed a series of photographs entitled Throwing Four Balls in the Air to Get a Square. In addition to a fun opportunity to think about parabolas, this work is provides an exciting perspective on process (in art as well as math!).
 

Here is the challenge I posed to my advanced algebra students:

On a fine October afternoon, around 3:40 pm, in fact, John Baldessari’s attempts to throw four balls in the air to get a square. As you can see, he didn’t do so well. We can do better!

Let’s assume he hopes to photograph the balls when each is at the highest point in its arc.

1.    What is this point called?
2.    The first ball peaks at the point (0,10). Write an equation to describe the ball’s height, h, as a function of t, time.
3.    Write equations for three other balls so that their vertices form a square with one corner at (0,10)