Question

Choose the graph of y < –x^2 + 4x + 5.

Answer 1

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.