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Lesson 7

1. Lesson 7

1.4. Discover

Mathematics 20-1 Module 4

Module 4: Quadratic Equations and Inequalities

 

Discover
 

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In this Discover section you will begin to explore how you can graph linear and quadratic inequalities in two variables.

 

Try This 1

 

Part A: Linear Inequalities

 

This is a play button that opens Linear Inequalities in Two Variables.

Screenshot reprinted with permission of ExploreLearning

Launch Linear Inequalities in Two Variables - Activity A, and then follow the steps below. Record your responses as you work through the steps.

 

 

 


 

Step 1: Graph a linear function by adjusting the sliders for m and b. Notice that the line divides the coordinate plane into two areas. Record the linear function you graphed.

 

Step 2: Choose the “≤” symbol. How does the graph change?

 

Step 3: Select “Show solution test.” A blue point appears on the coordinate plane. What are the coordinates of the point? Does the test show this point as a solution to the inequality? On which side of the line does the point appear?

 

Step 4: Now drag the point to another part of the coordinate plane. Is this new point a solution to the inequality?

 

Step 5: Continue to experiment with different points, lines, and inequalities.

 

Analysis

  1. How would you describe the location of the points that are solutions to the inequality?

  2. A graph of a linear function would be only a straight line. Why do you think a shaded region is included in the graph of a linear inequality?

  3. How does the graph of the line change when you change the inequality symbol from ≤ or ≥ to < or >?

  4. What happens if you drag the point onto a dashed line? Is the point a solution? Likewise, what happens if you drag the point onto a solid line? Is the point a solution?

  5. How would you instruct someone to sketch y > x + 3?

  6. Describe the relationship between the inequality symbol of an inequality and the relative position of the shaded area on the corresponding graph.

Part B: Quadratic Inequalities

 

This is a play button that opens Quadratic Inequalities in Two Variables.

Screenshot reprinted with permission of ExploreLearning

Launch Quadratic Inequalities in Two Variables - Activity A. Use your observations from Quadratic Inequalities in Two Variables to add to or revise your responses to Analysis questions 1 to 6. Then complete question 7.



  1. What differences, if any, are there between linear inequalities and quadratic inequalities?

course folder Save your responses in your course folder.

 

You will revisit these results in Explore.