An object is thrown straight upward from the ground with an initial speed of 30 feet per second. Its height (h) after t seconds is given by the equation h(t)= -5t^2+30t. Find the domain for h(t).

A.(-∞, 0)
B.(6, ∞)
C.(0, 6)
D.All real numbers

Question

An object is thrown straight upward from the ground with an initial speed of 30 feet per second. Its height (h) after t seconds is given by the equation h(t)= -5t^2+30t. Find the domain for h(t).

A.(-∞, 0)
B.(6, ∞)
C.(0, 6)
D.All real numbers

kainui · Answer

Domain is what all possible amounts your dependent variable can have. Since this variable is time, then it must start at 0, since you can't start at a negative time. Now moving forward, the height of the object changes and eventually it comes back down. So if we graph it, it'll look like this:

|dw:1383150853576:dw|

So there are two times when it hits the time axis (x-axis) right? But the height can't be less than 0, otherwise it's going underground. Which might be possible if we dig a hole, but in this case, it will stop because there's no hole there. They would have told us about it! So you need to solve for what the other time is that the height is 0 and that will be your domain.