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Lesson 7

1. Lesson 7

1.11. Lesson 7 Summary

Mathematics 20-1 Module 4

Module 4: Quadratic Equations and Inequalities

 

Lesson 7 Summary

 

This shows a photo of the Linked Hybrid mixed-use complex in Beijing, China.

© Shu He

In this lesson you investigated the following questions:

  • How are the properties of linear and quadratic inequalities in two variables related to their graphs?
  • How are linear and quadratic inequalities in two variables applied in design?

You explored linear inequalities and quadratic inequalities in two variables, and you learned how to graph these inequalities. To graph a linear or quadratic inequality, you must answer two key questions:

  • How do I graph the boundary?
  • How do I know which half-plane should be shaded?

The following table summarizes the properties of the graph of linear and quadratic inequalities given each type of inequality symbol.

 

 
  < ≤ > ≥
Boundary Type dashed solid dashed solid
Shading Relative to Boundary when y Is Isolated below below above above
Linear Inequality This shows a Cartesian plane and a dotted line with a positive slope going through the origin. The region below the line is shaded. This shows a Cartesian plane and a solid line with a positive slope going through the origin. The region below the line is shaded. This shows a Cartesian plane and a dotted line with a positive slope going through the origin. The region above the line is shaded. This shows a Cartesian plane and a solid line with a positive slope going through the origin. The region above the line is shaded.
Quadratic Inequality This shows a Cartesian plane with a dotted parabolic curve that has a negative x-intercept, a positive x-intercept, and is on the positive y-axis. The region below the parabola is shaded. This shows a Cartesian plane with a solid parabolic curve that has a negative x-intercept, a positive x-intercept, and an intercept on the positive y-axis. The region below the parabola is shaded. This shows a Cartesian plane with a dotted parabolic curve that has a negative x-intercept, a positive x-intercept, and an intercept on the positive y-axis. The region above the parabola is shaded. This shows a Cartesian plane with a solid parabolic curve that has a negative x-intercept, a positive x-intercept, and an intercept on the positive y-axis. The region above the parabola is shaded.

 

You also learned how to use the graphs of linear and quadratic inequalities to model problems involving constraints. These models are used in design and other industries to find possible solutions to problems.

 

In the final lesson of this module you will investigate solutions to quadratic inequalities in one variable. You will investigate both graphical and algebraic methods as solution strategies.