The height of a small rock falling from the top of a 124-ft-tall building with an initial downward velocity of –30 ft/sec is modeled by the equation h(t) = –16t^2 – 30t + 124, where t is the time in seconds. for which interval of time does the rock remain in the air?

t = 2

–2 < t < 0

0 < t < 2

t > 2

Option 3.

Step-by-step explanation:

The given function is

where, h(t) is the height of a small rock falling from the top of a 124-ft-tall building and t is the time in seconds.

It is a downward parabola.

Equate the function equal to 0, to find the time at which the rock touch the ground.

If , the according to the quadratic formula

Using quadratic formula, we get

Time cannot be negative. So, the rock remain in the air in the interval 0 < t < 2.

Therefore, the correct option is 3.