Question

A baseball is thrown upward and its height after t seconds can be described by formula h(t)=−16t^2+50t+5. Find the maximum height the ball will reach.

Answer 1

You need the vertex : )
Either factor to find the zeros then find the halfway point between them (sub in the x-value and solve for y) or use x = -b/(2a) to find the x-coordinate of the vertex : )
Your choice...

Answer 2

Just FYI, which may come in handy, the y-coordinate of the vertex is

(4ac-b^2)/(4a)
or
c - b^2/(4a)

Answer 3

Given:
h(t) = -16t^2 + 50t + 5.
g = 32ft/s^2
Vo = 50 ft./s

V = Vo + g*t = 0.
50 + (-32)t = 0,
t = 1.56 s.
h = -16*1.56^2 + 50*1.56 + 5 = 44.1 Ft.