A rocket is fired into the air with an initial velocity of 98 m/s. The height ( h ) of the rocket after t seconds is given by the expression h = 98t - 4.9t2.

Question

a. What the average rate of change over the first 2 seconds.
b. At what point does the rocket reach its maximum height? Show a graphical and algebraic solution.
c. Over what intervals is the rocket’s height increasing and decreasing?

Answer 1

(a) avg speed is (f(2)-f(0))/2 - distance/time
(b) as with any quadratic, the vertex is at x = -b/2a
(c) v = 98-9.8t
height is increasing where v>0

Answer 2

a. find the heights at t = 0 and t = 2, then perform a "slope" calculation of
average rate of change = change in distance/change in time

b. find the vertex of this parabola using the method you learned.
From the vertex you can read off the maximum height and when that max happened.

c. The time shown in the vertex tells you that, from 0 to the time of the max will be the time
when the height increases, after that the height will be decreasing.

This graph should confirm your answer.
http://www.wolframalpha.com/input/?i=plot+h+%3D+98t+-+4.9t2