Answer:
First graph
Step-by-step explanation:
The inequality is
y < -x² + 4x + 5
The line that separates the regions is the graph of the parabola y = -x² + 4x + 5
So, this is a parabola that opens down because the coefficient of x² is -1 and it is negative.
Therefore, the possible options are the first and the third graph
Then, let's see if the point (x, y) = (0, 0) belongs to the region
y < -x² + 4x + 5
0 < -0² + 4(0) + 5
0 < 5
Since the inequality is satisfied, the point (0, 0) belongs to the region and the answer is the first graph.