Question 853967
s(t) = -16t^2 + 54t
The maximum value for a function of the form
f(x) = ax^2 + bx + c , when a is negative occurs
when x = -b/(2a)
For our equation -b/(2a) = -54/(2(-16)) = 54/32 = 27/16
Substituting 27/16 for t in -16t^2 + 54t gives us
-16(27/16)^2 + 54(27/16)
-729/16 + 729/8
{{{-729/16 + (2/2)*(729/8)}}}
{{{-729/16 + (2*729/16)}}}
{{{729/16}}} or 45 9/16
See http://www.wolframalpha.com/input/?i=maximum+s%28t%29+%3D+-16t%5E2+%2B+54t