To find the rock's maximum height, we need to find the vertex of the parabolic function h(t) = -16t^2 + 80t + 30.
The t-coordinate of the vertex of a parabola given by the function h(t) = at^2 + bt + c is given by t = -b/(2a).
In this case, a = -16 and b = 80. So, t = -80 / (2 * -16) = -80 / -32 = 2.5.
To find the maximum height, plug t = 2.5 into the function h(t):
h(2.5) = -16(2.5)^2 + 80(2.5) + 30
h(2.5) = -16(6.25) + 200 + 30
h(2.5) = -100 + 200 + 30
h(2.5) = 130
Therefore, the rock reaches its maximum height of 130 feet at t = 2.5 seconds.
This same rock is thrown and it follows the path modeled by the function:
h(t) = -16t^2 + 80t + 30
When does the rock reach it's maximum height?
What is the maximum height it reaches?
1 answer
1 answer