Answer
See graph below.
Work Step by Step
The question asks to graph the solution set of the system of inequalities.
Here are some criteria for graphing inequalities:
1. If it is $\lt$ or $\gt$, then the graph must be dashed.
2. If it is $\leq$ or $ \geq$, then the graph must be solid.
3. If it is $\lt$ or $\leq$ (with y being isolated), then the shading is below, left, or inside the graph.
4. If it is $\gt$ or $\geq$ (with y being isolated), then the shading is above, right, or outside the graph.
Given:
1. $x^2 - y \leq 0$
$y \geq x^2$
2. $2x^2 + y \leq 12$
$y \leq 12 - 2x^2$
Graph $y =x^2$ and $y = 12 - 2x^2$ with a solid line.
Equation 1 is $\geq$, so the shading will be above the graph,
Equation 2 is $\leq$, so the shading will be below the graph,
The solution set is where the black and green areas overlap.
See graph below.
This solution set is bounded.
