Grab a pen and grid paper for this lesson. We will learn the tricks on graphing quadratic inequalities in two variables.

# Graphing quadratic inequalities in two variables

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Examples

**Graphing Quadratic Inequalities of Parabolas Opening Up**

Graph:

i) $y = \frac{1}{3}{x^2} - \frac{2}{3}x - \frac{8}{3}$

ii) $y \ge \frac{1}{3}{x^2} - \frac{2}{3}x - \frac{8}{3}$

iii) $y$ < $\frac{1}{3}{x^2} - \frac{2}{3}x - \frac{8}{3}$**Graphing Quadratic Inequalities of Parabolas Opening Down**

Graph:

i) $y = - {x^2} - 4x$

ii) $y$ > $- {x^2} - 4x$

iii) $y \le - {x^2} - 4x$