Note that the function is a quadratic with a negative lead coefficient. Hence the graph is a parabola opening downward and therefore the vertex is the maximum point. The value of the independent variable that gives the vertex value for any quadratic in the form
By the way, ask your teacher/instructor/professor what planet they were on when they conducted this experiment -- it certainly wasn't a planet in our solar system. Near the surface of planet Earth, the acceleration due to gravity is 32 feet per second per second, hence the height of a projectile as a function of time is given by:
where
The closest to -24 feet per second per second is Venus with a little over -29 feet per second per second.
You might also ask what machine was used to throw the projectile starting from not near the ground but exactly ON the ground at an initial velocity two and a half times faster than the fastest baseball pitches.
John
My calculator said it, I believe it, that settles it
