I find mentally it’s easier for some people to use the actual mirror. In this case ctrl+m->z->enter or left click. This is the same as scaling by -1 on an axis. S->z->-1->enter or LMB. Side note: mirroring(Either method) also flips the normals and is mirrored based on the chosen pivot point. That’s why I use 3D cursor and have it set to world origin. That way I don’t have to do the move downward afterwards.
To understand what is going on you need to know that in blender scale is multiplication. 1 times anything equals that thing. -1 times something is that thing but negative. so a vertex at 1.5 from pivot on z axis becomes -1.5 z or which ever axis you choose to scale on.