A set $\displaystyle C$ in $\displaystyle S$ is said to be convex if, for all $\displaystyle x$ and $\displaystyle y$ in $\displaystyle C$ and all $\displaystyle t$ in the interval $\displaystyle [0,1]$, the point $\displaystyle (1-t ) x + t y$ is in $\displaystyle C$. Convex set - Wikipedia, the free encyclopedia
Are you sure it is $\displaystyle X=\{(x_1, x_2) | x_2 - 3 \ge -x_1^2, x_1, x_2 \ge 0\} $ and not $\displaystyle X=\{(x_1, x_2) | x_2 - 3 \le -x_1^2, x_1, x_2 \ge 0\} $