Let S = \left \{ \begin{matrix} \left [ \begin{matrix} x \\ y \end{matrix} \right ] : x \geq 0 \text{and} y = x^{2} \end{matrix} \right \} . Show that the convex hull of S is the union of the origin and \left \{ \begin{matrix} \left [ \begin{matrix} x \\ y \end{matrix} \right ] : x \gt 0 \text{and} y \geq x^{2} \end{matrix} \right \} . See Figure 3.