Solve the inequality graphically
- Draw the graph of the left-hand side of the inequality in a coordinate system, .
- Draw the graph of the right-hand side of the inequality in the same coordinate system, .
- Mark where the graphs intersect. The graphs look like this:
- Read off the -values at the two points of intersection. From the figure you can see that the graphs intersect when and .
The parabola is above the line when is less than and when is greater than 2.
The points of intersection must be included in the solution, because the inequality has a “greater than or equal to” sign. The answer is thus and .