Let me give you one quick example. There are lots of others, but...
Suppose you toss a projectile in the air. The quadratic model might be something like:
The height (h) is a function of time (t).
Question: When does the maximum "occur" and what is the "value" at that time?
You need to find the vertex which is your "maximum point".
The x-coordinate of the vertex will tell you the time (t) when the maximum "occurred"
and the y-coordinate will tell you the "value" or height (h) at that time (t).
Maybe that helps. Hope so.