Answer:
The correct answer is A.
[tex]A(0,-2)[/tex]
Step-by-step explanation:
Method 1
You just have to plot each point on the graph.
The one that falls within the solution region is the correct choice.
From the graph, [tex]A(0,-2)[/tex] falls within the solution region.
See graph
Method 2
If you substitute the points into the inequalities, the only point that will satisfy both inequalities simultaneously is A.
The first inequality is
[tex]y\:<x^2+2[/tex]
If we substitute [tex]A(0,-2)[/tex], we get;
[tex]-2\:<\:(0)^2+2[/tex]
[tex]-2\:<\:2[/tex]
This statement is true.
The second inequality is
[tex]y\:>\:x^2-6[/tex]
If we substitute [tex]A(0,-2)[/tex], we get;
[tex]-2\:>\:(0)^2-6[/tex]
This gives,
[tex]-2\:>\:-6[/tex]
This statement is also true.
