The graph of y≥ x^2-4 is a region bounded by the graph of y=x^2-4. Notice that this parabola is a vertical translation down 4 units of the graph of its parent function y=x^2.
To determine the region to be shaded, we will test a point not on the graph. For simplicity, we will test (0,0). If the substitution produces a true statement, we will shade the region that contains the point. If not, we will shade the opposite region.
Since 0 is greater than -4, we shade the region containing (0,0).
Graphing y≤ - x^2+4
Similarly, the graph of y≤ - x^2+4 is a region bounded by the graph of y=- x^2+4. Notice that this parabola is a vertical translation up 4 units of the graph of y=- x^2.
To determine the region to be shaded, we test the point (0,0) as we did for the previous inequality. In this case, again, this point produces a true statement and therefore we shade the region containing (0,0).
