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Since the distance function tracks the height of the shell, and the shell was launched from the top of the hotel,where was the shell at t = 0?

You could take the derivative and evaluate at t = 0.
Or you could deconstruct the position function:

Notice that the distance function is a parabola. Use Algebra or Calculus to find the x-value of the vertex of this parabola.

Recall that a local maximum (or local minimum) is a y-value, not an x-value. After all, max and min mean highest and lowest, which are vertical measurements (y-axis measurements).

Given that s(0) ≠ 0, is it reasonable to assume that the ground is located at s(t) = 0?