PLEASE PLEASE help, none of my classmates and friends can figure this out we are suffering T_T

There are two parts to this solution:  The down part for the helmet, and the up part for the sound.  The down part has to be solved first, before the up part.

-- The helmet falls 78.4 meters.  How long does that take ?

In gravity,

Distance = (1/2) (acceleration) (Time²)

78.4 m = (1/2) (9.8 m/s²) (Time²)

Time² = (78.4 m) / (4.9 m/s²)

Time² = 16 sec²

Time = 4 seconds.

-- The crew heard the sound of helmet hitting the ground 4.23 seconds after their buddy dropped it.

We just calculated that it took 4 seconds for it to hit the ground.

So it took 0.23 second for the sound of the clunk to propagate the 78.4 meters back up to them.  What's that speed ?

Speed = (distance) / (time)

Speed = (78.4 m) / (0.23 sec)

Speed = 340.9 m/s

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .