(a) A generic quadratic expression is often written
ax² +bx +c
Then the "a" and "b" in the expression -b/(2a) represent the coefficients of the squared term and the linear term, respectively. In your quadratic expression, the variable is "t", not "x", but that makes no difference. You have
a = -16
b = 96
Then the time (t) at the maximum height is
t = -b/(2a)
t = -96/(2(-16)) = 96/32 = 3
The ball is highest 3 seconds after being fired.
(b) Evaluating h for t=3, we get
h = -16*3² +96*3 +11
h = -144 +288 +11
h = 155
The maximum height of the ball is 155 ft.