SOLUTION: The altitude of a rocket t seconds after launch is given by the function h(t)=-6t^2+32T+3 where h is the height in feet. how long after the launch will it take for the rock

Question 1140923: The altitude of a rocket t seconds after launch is given by the function
h(t)=-6t^2+32T+3 where h is the height in feet.
how long after the launch will it take for the rocket to reach it's maximum height?

please and thank you
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

here you have downward parabola, and its maximum is vertex (,)
so, rewrite your equation in vertex form

........

vertex is at (,)
the rocket to reach it's maximum height in or seconds

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
h(t)= -6t^2 +32T +3
:
be consistent in the formula, I assume T = t, then
:
h(t)= -6t^2 +32t +3
:
the t^2 coefficient does not look right(should be -16 instead of -6) but I will use the formula as you have stated it
:
the x-axis is time and the y-axis is height
:
time when maximum height is reached is the x-coordinate of the parabola's vertex
:
Note the graph of this equation is a parabola that curves downward
:
time when maximum height is reached = -b/2a = -32/2(-6) = 32/12 = 8/3 = 2 and 2/3 seconds
:
Note general form of a quadratic is ax^2 +bx +c
:
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