Answer
The solution set is the region shaded GRAY
Work Step by Step
We will graph the solution region for each inequality.
Quadratic functions have a parabola for a graph.
To graph a line, we need two points...unless we know it is vertical or horizontal.
1. (red)
Border:$\quad y=x^{2}-4\quad $solid line ( sign is $\geq )$,
The curve is a parabola that opens up $(a=1>0)$ , with
vertex: $(0,-4)$
x-intercepts:
$0=x^{2}-2^{2}$
$0=(x+2)(x-2)$
x-intercepts:$ \quad \pm 2$
Testing $(0,0):\quad 0 \geq 0^{2}-4\quad?$
Yes, shade the region containing $(0,0)$
2 (blue)
$x-y=2 \quad $solid line ( sign is $\geq )$,
x-intercept:$\quad x-0=2\quad$ point: ($2,0)$
y-intercept:$ \quad 0-y=2\quad$ point: ($0,-2)$
Testing $(0,0)$:$\quad 0-0 \geq 2 \quad ?$
No, shade the region not containing (0,0)
The solution set is the region with BOTH shadings.
The solution set is the region shaded GRAY