The term "Smiley face curve" is not widely recognized in established academic, scientific, or technical literature. Accurate information is not confirmed.
It may informally refer to a graphical curve resembling the shape of a smiley face, typically observed when a parabola opens upward and is stylized with endpoints or annotations to resemble eyes and a curved mouth. In mathematics or data visualization, such a depiction might appear in educational contexts to illustrate quadratic functions or to engage students through visual metaphors, but it does not denote a formal mathematical concept.
In other contexts, the phrase could be used descriptively in design, art, or popular culture to refer to any smooth, upward-curving line evoking the familiar expressive icon of a smiley face. However, no peer-reviewed or authoritative sources define or reference "smiley face curve" as a standardized term.
Until verifiable sources confirm its use in a specific domain, the phrase remains informal and context-dependent.