Question

The x-coordinate (or t-coordinate) of the vertex is
and represents

.
The y-coordinate (or h-coordinate) of the vertex is
and represents

.

Answer 1

The t-coordinate (or x-coordinate) of the vertex is t = −b/(2a) and represents the time (or x-value) at which the parabola reaches its maximum (if a < 0) or minimum (if a > 0).

The h-coordinate (or y-coordinate) of the vertex is h = f(−b/(2a)) = c − b^2/(4a) (for f(t)=at^2+bt+c) and represents the maximum (if a < 0) or minimum (if a > 0) value of the function (e.g., the maximum/minimum height).

(Equivalently, if the quadratic is written in vertex form a(t−h)^2+k, the vertex is (h,k), so the t-coordinate is h and the h-coordinate is k.)