About Second Degree Inequalities:
When we graph a non-linear inequality, we start with the boundary. We graph the boundary by replacing the inequality symbol with an equality symbol and graphing the resulting equation. We can use a test point to find and shade the appropriate region. When we encounter a system of non-linear inequalities, we graph each inequality and shade the overlap of the graphs as our solution to the system.
Test Objectives
- Demonstrate the ability to graph the boundary of a non-linear inequality
- Demonstrate the ability to graph a non-linear inequality
- Demonstrate the ability to graph a system of non-linear inequalities
#1:
Instructions: Graph each non-linear inequality.
a) $$y > x^2 - 3x$$
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#2:
Instructions: Graph each non-linear inequality.
a) $$(x - 2)^2 + (y + 3)^2 < 4$$
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#3:
Instructions: Graph each non-linear inequality.
a) $$\frac{(x - 1)^2}{1}+ \frac{(y + 2)^2}{4}> 1$$
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#4:
Instructions: Graph each non-linear system of inequalities.
a) $$y > -x^2 - 5x - 4$$ $$3x + 4y < 2$$
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#5:
Instructions: Graph each non-linear system of inequalities.
a) $$x^2 + y^2 < 16$$ $$\frac{x^2}{4}- \frac{y^2}{25}≥ 1$$
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Written Solutions:
#1:
Solutions:
a)
Watch the Step by Step Video Solution
#2:
Solutions:
a)
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#3:
Solutions:
a)
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#4:
Solutions:
a)
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#5:
Solutions:
a)
