SOLUTION: The altitude in feet of a toy rocket t seconds after launch is given by the function S(t) = -16t^2 + 128t. What is the maximum altitude reached by the rocket? How long does

Algebra ->  Functions -> SOLUTION: The altitude in feet of a toy rocket t seconds after launch is given by the function S(t) = -16t^2 + 128t. What is the maximum altitude reached by the rocket? How long does      Log On


   



Question 181630: The altitude in feet of a toy rocket t seconds after launch is given by the function S(t) = -16t^2 + 128t.
What is the maximum altitude reached by the rocket?

How long does it take for the rocket to reach this maximum altitude?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
S%28t%29+=+-16t%5E2+%2B+128t
With a parabola, the maximum or minimum occurs wher
t+=+%28-b%29%2F%282a%29 when the general formula is
S%28t%29+=+at%5E2+%2B+bt+%2B+c
a+=+-16
b+=+128
%28-b%29%2F%282a%29+=+%28-128%29%2F%282%2A%28-16%29%29
%28-b%29%2F%282a%29+=+4sec
In 4 sec the rocket will reach it's maximum altitude
S%28t%29+=+-16t%5E2+%2B+128t
S%284%29+=+-16%2A4%5E2+%2B+128%2A4
S%284%29+=+-128+%2B+128%2A4
S%284%29+=+384 ft
The maximum altitude is 384 ft