SOLUTION: The equation H(T)=-16x^2+64x+9 models the height, H , in feet, of a model rocket t seconds after it has been launched from 9 feet above the ground. How many seconds after launchin

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Question 1205519: The equation H(T)=-16x^2+64x+9 models the height, H , in feet, of a model rocket t
seconds after it has been launched from 9 feet above the ground. How many seconds after launching the rocket will it reach its maximum height?
A.1 seconds
B.2 seconds
C.2.5 seconds
D.3 seconds
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The equation H(T)=-16x^2+64x+9 models the height, H , in feet, of a model rocket t
seconds after it has been launched from 9 feet above the ground. How many seconds after launching the rocket will it reach its maximum height?
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There are no T's in the function.
Assuming you mean H(T)=-16T^2 + 64T + 9
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At the apogee, max height, the vertical speed is zero (0).
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H(T)=-16T^2 + 64T + 9
H'(T) = -32T + 64 = 0 ----- THE 1ST DERIVATIVE
T = 2 seconds

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

H%28t%29=-16x%5E2%2B64x%2B9 this is a parabola that opens down
so we can find t coordinate of the maximum using the formula
t=-b%2F2a where b=64 and a=-16
t=-64%2F%282%28-16%29%29
t=-64%2F%28-32%29
t=2

answer:
B.2+seconds