The sign of the parabola

For second-degree inequalities we can use the parabola: the sign of $ax^2+bx+c$ is read directly from the graph, according to whether the parabola lies above or below the $x$-axis. Everything comes down to three pieces of information:

1. the sign of $a$ (concavity upwards or downwards);
2. the sign of the discriminant $\Delta = b^2-4ac$ (number of zeros);
3. if $\Delta\ge 0$, the positions of the two zeros on the $x$-axis.

Links

Topics: Inequalities
Concepts: Concavity · Discriminant · Second-degree inequality · Parabola
Skills: Interpreting a graph