Question
This same rock is thrown and it follows the path modeled by the function: h(t) = −16t2 + 80t + 30
Answers
GPT 3.5
To find the maximum height the rock reaches, we need to find the vertex of the parabolic function h(t) = -16t^2 + 80t + 30.
The t-coordinate of the vertex is given by t = -b / 2a, where the function is in the form h(t) = at^2 + bt + c.
In this case, a = -16 and b = 80, so t = -80 / 2(-16) = -80 / -32 = 2.5.
Plugging t = 2.5 back into the function h(t), we get:
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 maximum height the rock reaches is 130 feet.
The t-coordinate of the vertex is given by t = -b / 2a, where the function is in the form h(t) = at^2 + bt + c.
In this case, a = -16 and b = 80, so t = -80 / 2(-16) = -80 / -32 = 2.5.
Plugging t = 2.5 back into the function h(t), we get:
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 maximum height the rock reaches is 130 feet.