In order to graph this inequality, first let's graph the corresponding equation.
To do so, let's find 5 points that are solutions to the equation:
[tex]\begin{gathered} y=(x-2)^2+3 \\ \\ x=0\colon \\ y=4+3+7 \\ x=1\colon \\ y=1+3=4 \\ x=2\colon \\ y=0+3=3 \\ x=3\colon \\ y=1+3=4 \\ x=4\colon \\ x=4+3=7 \end{gathered}[/tex]
Since the symbol of the inequality is ">", the solution region is above the parabola, and the parabola itself is not part of the solution (therefore we draw it with a dashed line).
So we have:
