Question

Which graph shows the correct solution to the linear-quadratic system of inequalities below?

mc019-1.jpg
mc019-2.jpg
mc019-3.jpg
mc019-4.jpg
mc019-5.jpg

Answer 1

I don't see the system of inequalities or the graphs — only the filenames. Please either paste the inequalities here or upload the problem image (or describe the graphs and the inequalities). Then I can check which pictured graph is correct.

If you want to check it yourself, here are quick steps you can follow:

1. Identify the two boundary curves (the quadratic y = ax^2 + bx + c and the line y = mx + b).
2. Replace each inequality with an equality to draw the boundary. Use a solid curve if the inequality is ≤ or ≥, dashed if < or >.
3. Find their intersection points by solving ax^2 + bx + c = mx + b (bring all terms to one side and solve the quadratic). These x-values split the plane into regions.
4. Pick a test point in each region (commonly (0,0) if it's not on a boundary) and check both inequalities to see whether that region satisfies the system.
5. Shade the region(s) that satisfy both inequalities — the correct graph will have exactly that shaded region with the correct boundary styles.

If you paste the inequalities or upload the images, I’ll identify which mc019-*.jpg is correct.