Using the graph at the left, it shows the height h in feet of a small rocket t seconds after it is launched. The path of the rocket is given by the equation:
h(t) = -16^2 + 128t
What is the maximum height of the rocket
To find the maximum height of the rocket, we need to determine the vertex of the parabolic equation h(t) = -16t^2 + 128t.
The vertex of a parabola in the form y = ax^2 + bx + c is given by the equation x = -b/2a.
In this case, a = -16 and b = 128. Plugging these values into x = -b/2a:
t = -128 / (2*(-16))
t = -128 / (-32)
t = 4
Therefore, the maximum height of the rocket occurs at t = 4 seconds. To find the maximum height, we can plug t = 4 into the equation h(t):
h(4) = -16(4)^2 + 128(4)
h(4) = -16(16) + 128(4)
h(4) = -256 + 512
h(4) = 256
So, the maximum height of the rocket is 256 feet.