When a curve is always negative, the graph only resides below the x-axis all the time. This implies that the curve must be sad face. Smiley face curves cannot ever be “always below the x-axis” because it will always go up at both ends.

Also, the fact that the graph only resides below the x-axis means that the curve will never ever cut the x-axis, so the equation will not have any real roots at all.