Question

A model rocket is launched from the roof of a building. Its flight path is modeled by the table below, where h(t) is the height of the rocket above the ground in meters and t is the time after the launch in seconds. What is the rocket’s initial height?
t 1 2 3 5
h(t) 11 23 45 119

Answer 1

A model rocket is launched from the roof of a building. Its flight path is modeled by h equals minus 5 t squared plus 30 t plus 10 where h is the height of the rocket above the ground in meters and t is the time after the launch in seconds. 
What is the rocket's maximum height?
How long before the rocket reaches the ground?
***
h=-5t^2+30t+10
complete the square:
h=-5(t-6+9)+45+10
h=-5(t-3)^2+55
This is an equation of a parabola that opens down with vertex at (3,55)
maximum height=55m
..
when rocket reaches the ground, h=0
-5t^2+30t+10=0
5t^2-30t-10=0
solve by quadratic formula:

-b+or-√b^2-4ac
_______
2a


a=5, b=-30, c=-10
ans: t≈6.32 sec
maximum height? 55m
How long before the rocket reaches the ground? 6.32sec