Answer
Please see the graph.
Work Step by Step
Green line: $x^{2}+y^{2}<4$
Orange line: $x\ge0$
Purple line: $y\ge x^{2}-1$
We use the point $(0,0)$ to determine what sides of the lines to shade. The orange and purple lines will be solid (since we have greater than or equal to signs), while the green line will be dotted (since it has a less than sign).
$x^{2}+y^{2}<4$
$0^{2}+0^{2}<4$
$0 + 0 < 4$
$0 < 4$ (true, so we shade the side of the line with the point)
$x \ge 0$
$0 \ge 0$ (true, so we shade the side of the line with the point)
$y\ge x^{2}-1$
$0\ge 0^{2}-1$
$0 \ge 0 - 1$
$0 \ge -1$ (true, so we shade the side of the line with the point)
The overlap of the three graphs is the solution set to the set of inequalities.
