Use mirror formula to show that convex mirror always forms a virtual image independent of object's location.

Answer 1

u is always negative.
Let u = -x for some positive number x.
f of a convex mirror is positive.
1/f = 1/u + 1/v
1/v = 1/f - 1/u = 1/f + 1/x = (f + x)/fx
v = fx/(f + x)
f and x are both positive. So fx and f + x are also positive.
Thus v is positive.

Hope this helps.

[e-mail]