How long does it take to reach maximum height

Question

A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t) = −4.9t^2 + 24t + 8. How long does it take to reach maximum height?

Answer 1

the maximum height occurs at the vertex so all you need is the x coordinate of the vertex which is at -b/2a which is -24/(2)(-4.9)= 2.449seconds