what is the maxiumum height of h(t)=-4.9(t-5)^2+124

Answer 1

h(t) = -4.9(t-5)^2 + 124

take the derivative and set equal to zero

h'(t) = -9.8(t-5) = 0

-9.8t + 49 = 0

t = 49/9.8 = 5 seconds

plug that back into the original equation

h(5) = -4.9(5-5)^2 + 124 = 124 meters

But you could have seen this either by graphing or realizing this is a downward opening parabola, so it's maximum is the vertex, and the initial height is the maximum height, as it's going down, only getting to lower heights.

you know the units are meters because 9.8 meters per second per second is the deceleration due to gravity (at sea level). Had it been -32 that would be feet.