The minimum or maximum of a parabola always occurs at its vertex. Since m is positive, the parabola opens upwards in a " U " shape, which means we're dealing with the parabola's minimum at its vertex. Since expanding f gives us a vertex form of f(x)=m[(x−m)2−1]=m(x−m)2−m, the vertex is at (m,−m). Therefore, the parabola's minimum occurs at (m,−m).