Answer:
The graph of given inequality is attached below.
Step-by-step explanation:
The given inequality is
[tex]y<x^2+2[/tex]
The related equation of the of the given inequality is
[tex]y=x^2+2[/tex] .... (1)
The related curve is dotted because the sign of inequality is <. The points on the curve are not included in the solution set.
It is a quadratic equation. So, the graph of related equation is a parabola.
The vertex form of a parabola is
[tex]y=(x-h)^2+k[/tex] .... (2)
From (1) and (2), we get
[tex]h=0,k=2[/tex]
The vertex of the parabola is at (0,2).
At x=1,
[tex]y=(1)^2+2=3[/tex]
At x=-1,
[tex]y=(-1)^2+2=3[/tex]
It means the graph if passing through (1,3) and (-1,3).
Check the inequality by (0,0),
[tex](0)<(0)^2+2[/tex]
[tex]0<2[/tex]
This statement is true, it means (0,0) is in the shaded region.
The graph of given inequality is attached below.
