We apply sign convetions to the measurements we make and not to the general formula.
The mirror formula is same for all the mirrors, its given by 1/v + 1/u = 1/f.
If we apply sign convention over here itself it'll be changed. Sign conventions are applied on the magnitude of measurements and not on the general formula. When you will solve the problem you will automatically get the focal lengths as negative, obeying the sign convention.
Hope this helps.