Answer
The graph is shown below:
Work Step by Step
Let us consider the given inequalities
$\begin{align}
& y>{{x}^{2}} \\
& x+y<6 \\
& y< x+6
\end{align}$
We see that the first inequality is incorrect for the test point $\left( 0,0 \right)$; therefore, the shaded region will not contain the test point; the second and third expressions are correct for the test point $\left( 0,0 \right)$, so the origin will be included for these inequalities.
The final graph of the given inequalities is plotted below.
