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3 3 polynomial inequalities in two variables

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3 3 polynomial inequalities in two variables

  1. 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. 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. 3. Example 1 • Sketch the graph of y > x2 – 2x – 8
  4. 4. Extra Example 1 • Sketch the graph of |x + 1| > 3
  5. 5. Extra Example 2 • Sketch the graph of y  x3 + 2x2
  6. 6. You Try! • Sketch the graph of y > 3x2 + 6x - 2
  7. 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. 8. Example 2 • Graph the solution set of the inequalities y  4 – x2 and y > x + 2. (And show where they intersect)
  9. 9. Extra Example 1 • Graph the solution set of the system: y > -x y < (x + 2)2
  10. 10. You Try! • Graph the solution set of the system: y  6 – x2 2x – y  -3

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