Question

A rock is tossed straight up into the air. The height h (in feet) t seconds after it is tossed is given by
the function:

h(t)=-16t^2+100.4t+5.1

(a) Make a table of values for 0 to 10 seconds.
(b) Graph the function.
(c) What is the initial height of the rock?
(d) When did the rock reach its maximum height? What is that height?
(e) At what time did the rock hit the ground?

Answer 1

No one, like no one, uses feet any more for physics problems but anyway

It is a parabola (uppside down, sheds water)

c) at t = 0, h = 5,1

d) find the vertex by completing the square or know that the rock is at the top when the velocity is zero which is when
-32 t + 100.4 = 0
t = 3.14 seconds to top
h = -16(3.14)^2 +100.4(3.14) + 5.1
= -158 + 315 +5.1 = 162 feet

e) solve quadratic for roots and use positive t
3.14+/-3.19
use t = 6.33 seconds