Think of a convex mirror as a safety mirror in a parking garage; it always forms a smaller, virtual, and erect image behind the mirror, which is why the image distance is positive.

UVF-Sign: Convex mirror? Focal length is positive. Object distance? Always negative.

The mirror formula is given by $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$. For a convex mirror, the focal length $f$ is positive (+8 cm) and the object distance $u$ is always negative (-12 cm) due to sign convention. Substituting these values: $\frac{1}{8} = \frac{1}{v} + \frac{1}{-12}$, which simplifies to $\frac{1}{v} = \frac{1}{8} + \frac{1}{12} = \frac{3+2}{24} = \frac{5}{24}$. Thus, $v = \frac{24}{5} = +4.8$ cm.

Always remember the sign convention: light travels left to right, so distance against light is negative, and with light is positive.