Somewhere you're given the equation for height as a function of time:
... h(t) = -16t² + v₀·t . . . . . . where v₀ is the initial vertical velocity in ft/s
For v₀ = 224, this becomes
... h(t) = -16t² + 224t
And this can be rewritten in vertex form as
... h(t) = -16(t² + 14t)
... h(t) = -16(t² + 14t +7²) +16·7² . . . . . complete the square (add the square of half the t coefficient inside parentheses; add the opposite of that amount outside parentheses)
... h(t) = -16(t +7)² + 784
The vertex of this downward-opening parabola is (7, 784), so ...
The rocket reaches its maximum height at 7 seconds.
The maximum height of the rocket is 784 feet.
