There only exist an inverse function if the original function doesn't change its monotony. Since your function first is monotonically decreasing and after the vertex it is monotonically increasing you have to split the domain into parts such that the function is monotonic.

1. Calculate the coordinates of the vertex by completing the square:

V

Thus the vertex is at

2. Now you can split your function into two monotonic parts:

For each of these parts exist an inverse function.

3. Swap the variables and solve the equation for y:

Swap the domain and range of the original function too that you get the domain and range of the inverse function(s):

4. Finally you have:

5. The graphs of the original function and its inverse functions must be reflections over the line y = x (firste median?). See attachment.