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