Find the roots and sketch the parabola. Read where the curve is above or below the horizontal axis. Include roots for <= or >=, and exclude them for < or >. Example x2-x-6=(x+2)(x-3). The parabola opens upward, so x2-x-6 0 for -2 <= x 3, and x2-x-6>0 for x<-2 or x>3. If the leading coefficient is negative, the sign regions reverse. A repeated root does not change the sign: (x-2)2 0 holds only at x=2.

Find the roots and sketch the parabola. Read where the curve is above or below the horizontal axis. Include roots for \(\le\) or \(\ge\), and exclude them for \(<\) or \(>\).

\(x^2-x-6=(x+2)(x-3)\). The parabola opens upward, so \(x^2-x-6\le0\) for \(-2\le x\le3\), and \(x^2-x-6>0\) for \(x<-2\) or \(x>3\).

If the leading coefficient is negative, the sign regions reverse. A repeated root does not change the sign: \((x-2)^2\le0\) holds only at \(x=2\).

Quadratic Functions, Equations and Inequalities

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Quadratic inequalities

Quadratic inequalities