Using the graph at the left, it shows the height in feet of a small rocket seconds after it is launched. The path of the rocket is given by the equation:
h(t)=-16t^2+128
What is the maximum height of the rocket?
(click on the graph)
The maximum height of the rocket can be found by looking at the vertex of the parabolic graph. The vertex is the highest point of the graph, which represents the maximum height reached by the rocket.
In this case, the equation of the path of the rocket is given as h(t) = -16t^2 + 128. The t-coordinate of the vertex can be found using the formula t = -b/2a, where a = -16 and b = 0 (since there is no linear term in the equation).
t = -0 / 2(-16)
t = 0 / -32
t = 0
Therefore, the rocket reaches its maximum height at t = 0 seconds. Now, substitute t = 0 back into the equation to find the maximum height:
h(0) = -16(0)^2 + 128
h(0) = 128
So, the maximum height of the rocket is 128 feet.