JAMB 2011 · UTME · Q18

Which of the following diagrams represents the solution of the inequalities $y \le x - 2$ and $y \ge x^2 - 4$ ?

In each diagram the curve is y = x² − 4 and the straight line is y = x − 2.

Worked solution (try it first)

$y \le x - 2$ is the region on or below the straight line.
$y \ge x^2 - 4$ is the region on or above the parabola, inside the U.
They meet where $x^2 - 4 = x - 2$ , that is $x^2 - x - 2 = 0$ , so $(x + 1)(x - 2) = 0$ and $x = -1$ or $x = 2$ .
The solution is the region below the line and above the parabola from $x = -1$ to $x = 2$ , which is diagram A.