3-3 Polynomial Inequalities in Two Variables

Objectives:1. Graph polynomial inequalities in two variables.2. Graph the solution set of a system of inequalities.

2-Variable Inequalities•Since inequalities have many solutions,

we shade the region where solutions lie.

•To graph non-linear inequalities:▫Try to factor and plot zeros.▫For parabolas: use zeros, vertex, and/or y-int.

•Don’t forget solid/dashed lines!

Example 1•Sketch the graph of y > x2 – 2x – 8

Extra Example 1•Sketch the graph of |x + 1| > 3

Extra Example 2•Sketch the graph of y x3 + 2x2

You Try!•Sketch the graph of y > 3x2 + 6x - 2

Systems of Inequalities•Find where the solution sets overlap.•Shade that area darker.

•For non-linear systems:•Need to show intersection points of the

functions.•Can find algebraically (by setting them

equal) or on calculator.

Example 2•Graph the solution set of the inequalities

y 4 – x2 and y > x + 2. (And show where they intersect)

Extra Example 1•Graph the solution set of the system: y > -x y < (x + 2)2

You Try!•Graph the solution set of the system:

y 6 – x2

2x – y -3