college algebra
posted by Anonymous on .
If a rocket is propelled upward from ground level, its height in meters after t seconds is given by h=9.8t^2+88.2t. During what interval of time will the rocket be higher than137.2m?
Do I set it up like this?
9.8(1)^2+88.2(1)+137.2 = 215.6
Then h=b/2a=9.8/215.6=22m
137.2+22=159
Thanks for your help.

Not quite. You found (sort of) when the height is greatest (the vertex of the parabola). That was not the question.
You have
h=9.8t^2+88.2t
when is h=137.2?
(Aside. You sure about that 9.8? h = vt  1/2 at^2 and a = 9.8)
137.2 = 9.8t^2 + 88.2t
t = 2,7
So, at those two times, h=137.2
Knowing what you do about the shape of parabolas, and that this one opens downward, h > 137.2 between those two values, so
2 < t < 7