A rock is thrown from one side of a river to another. The function h(t) = −16t2 + 80t + 30 gives the height in inches of the rock t seconds after it has been thrown.
This same rock is thrown and it follows the path modeled by the function
h(t) = -16t^2 + 80t + 30.
To find the height of the rock at any given time t, we simply plug in the value of t into the function h(t) and solve for h.
For example, to find the height of the rock after 3 seconds, we would plug in t = 3 into the function:
h(3) = -16(3)^2 + 80(3) + 30
h(3) = -16(9) + 240 + 30
h(3) = -144 + 240 + 30
h(3) = 126
Therefore, after 3 seconds, the height of the rock would be 126 inches.
We can similarly find the height of the rock at any other time by plugging in that value of t into the function h(t).