Answer:
Graphing the inequalities, we have;
Explanation:
Given the system of quadratic inequalities;
[tex]\begin{cases}y<-x^2-x+8 \\ y>x^2+2\end{cases}[/tex]
Graphing the quadratic inequalities;
for the first quadratic inequality;
[tex]\begin{gathered} y<-x^2-x+8 \\ at\text{ x=0} \\ y<8 \\ (0,8) \\ at\text{ x=-0.5} \\ y<-(-0.5)^2-(-0.5)+8 \\ y<8.25 \\ (-0.5,8.25) \\ at\text{ x=-2} \\ y<-(-2)^2-(-2)+8 \\ y<-4+2+8 \\ y<6 \\ (-2,6) \\ at\text{ x=}2 \\ y<-(2)^2-(2)+8 \\ y<-4^{}-2+8 \\ y<2 \\ (2,2) \end{gathered}[/tex]
For the second quadratic inequality;
[tex]\begin{gathered} y>x^2+2 \\ at\text{ x=0} \\ y>2 \\ at\text{ x=2} \\ y>(2)^2+2 \\ y>6 \\ (2,6) \\ at\text{ x=-2} \\ y>(-2)^2+2 \\ y>6 \\ (-2,6) \end{gathered}[/tex]
Graphing the two inequalities using the points derived above.
Note that both inequalities would be dashed lines because of the inequality sign, and the shaded part will be according to the sign.
Graphing the inequalities, we have;
