1. 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. 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!

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

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

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

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

7. 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.

8. Example 2
• Graph the solution set of the inequalities
y  4 – x2 and y > x + 2.
(And show where they intersect)

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

10. You Try!
• Graph the solution set of the system:
y  6 – x2
2x – y  -3