Question

Please show work on how to get the points we graph

Answer 1

Graphing the inequalities, we have;

Step-by-step explanation:

Given the system of quadratic inequalities;

`\begin{cases}y<-x^2-x+8 \\ y>x^2+2\end{cases}`

Graphing the quadratic inequalities;

for the first quadratic inequality;

`\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}`

For the second quadratic inequality;

`\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}`

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;