8.1 and 8.2 Inequalities in 2 Variables
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8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables 1 May 27, 2013 8 Inequalities
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Transcript of 8.1 and 8.2 Inequalities in 2 Variables
8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables
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May 27, 2013
8 Inequalities
8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables
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May 27, 2013
10 2 3 4 5 6 7 8 9 1012345678910
1. Graph x = 9
2. Graph x ≥ 9
3. Graph x < 9
8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables
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May 27, 2013
Linear Inequalities in 2 Variables
"An inequality in the two variables x and y describes a region in the Cartesian plane. The ordered pair (x, y) is a solution to a linear inequality if the inequality is true when the values of x and y are substituted into the inequality. The set of points that satisfy a linear inequality can be called the solution set, or solution region."
8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables
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May 27, 2013
Steps for Graphing Inequalities
1. Draw the line2. Choose a reasonable test point3. Test the point and ask, "Does it satisfy the inequality?"4. Use the result from Part 3 to shade in the appropriate region
8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables
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May 27, 2013
Example: Graph 10x 5y > 0
8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables
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May 27, 2013
Example: Determine if the point (2, 4) is a part of the solution of the line 2x + 3y ≤ 6
8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables
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May 27, 2013
Example: Write an inequality to represent the following graph:
8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables
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May 27, 2013
8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables
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May 27, 2013
Quadratic Inequalities in Two Variables
Exact same procedure as linear inequalities except now you have a quadratic instead of a line!
1. Draw the quadratic function.2. Choose a reasonable test point3. Test the point and ask, "Does it satisfy the inequality?"4. Use the result from Part 3 to shade in the appropriate region
8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables
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May 27, 2013
Example: Graph the following inequality
8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables
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May 27, 2013
Example: Graph the following inequality
8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables
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May 27, 2013
Example: Graph the following system of inequalities.
1. Graph the boundary lines2. Find the region3. The overlapping region is the final solution
8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables
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May 27, 2013
Example: Graph the following system of inequalities.
1. Graph the boundary lines2. Find the region3. The overlapping region is the final solution
8.1 and 8.2 Linear and Quadratic Inequalities in 2 Variables
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May 27, 2013
HOMEWORKOn a piece of graph paper, find the solution region for the following system of inequalities:
Also...page 496, #1, 3, 4, 6cd, 7b
