A rock is thrown from one side of a river to another. The function h(t) = −16t2 + 80t + 30
ℎ
is a quadratic function that represents the height of the rock above the water at time t seconds after it is thrown. The initial height of the rock is 30 feet above the water.
The axis of symmetry of the function can be found using the formula t = -b/2a, where a = -16 and b = 80.
So, t = -80 / 2(-16) = -80 / -32 = 2.5 seconds.
This means that the rock reaches its maximum height after 2.5 seconds.
To find the maximum height of the rock, substitute 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 feet.
Therefore, the rock reaches a maximum height of 130 feet after 2.5 seconds.