Answer: A
Explanation:
For this problem, we can automatically eliminate B and D. We know this because of the inequality. The inequality is less than or equal to. anything that has an equal to sign is a solid line because any point on the line itself is a solution. If it was a < sign, it shows that the solution is less than, and not equal to. Therefore, the line would be dotted/dashed.
Now that we have figured out what type of line we have, we can see where the shading is located. To do so, we must make all the same variables go on the same side to see the equation.
y ≤ x²-4x+2
From this, we see that y is less than or equal to. This tells us that the shading is under the line. Under the line, y goes towards negative infinity, which makes y less than the line. Above the line, y goes towards positive infinity, which makes y greater than the line. That would make the inequality y≥x²-4x+2. Therefore, A is the correct answer.