The function h(t) = 2 + 50t -1.862t^2, where h(t) is the height in metres and t is the time in seconds, models the height of a golf ball above the planet Mercury's surface during its flight.
A) What is the maximum height reached by the ball (i got 1165.8, is this correct)
B) how long will the ball be above the surface of Mercury ( not sure how to do)
the vertex is reached at t = -b/2a = 25/1.862 = 13.426
h(13.426) = 337.661
Your value is way high.
To find time in flight, just find when h=0. Up till then, the ball is above the surface.
2 + 50t -1.862t^2 = 0
t = 26.89