Graphing Nonlinear Inequalities and Circles

This lesson explains how to graph a nonlinear inequality in two variables, specifically x squared plus y squared is greater or equal to 9. The process involves converting the inequality to an equation to graph it as a circle on an XY plane. The radius is determined by the square root of the constant, which is 3 in this case. The lesson covers the concept of non-strict inequalities and demonstrates how to test points to determine which region to shade, ultimately shading the area outside the circle where the inequality holds true.

What is the inequality that needs to be graphed in this lesson?

• x^2 + y^2 < 9

• x^2 + y^2 > 9

• x^2 + y^2 ≤ 9

• x^2 + y^2 ≥ 9

What is the first step in graphing the given inequality?

• Plotting points on the graph

• Changing the inequality to an equation

• Shading the region

• Testing a point

What shape does the equation x^2 + y^2 = 9 represent?

• Ellipse

• Hyperbola

• Parabola

• Circle

How is the radius of the circle determined from the equation x^2 + y^2 = 9?

• By subtracting 1 from the constant

• By multiplying the constant by 2

• By taking the square root of the constant

• By dividing the constant by 2

Which points are plotted to form the circle?

• (0, 0), (3, 3), (-3, -3), (3, -3)

• (0, 0), (3, 3), (-3, 0), (0, 3)

• (0, 0), (3, 0), (0, 3), (-3, -3)

• (0, 3), (3, 0), (-3, 0), (0, -3)

What type of line is used to connect the points on the circle for a non-strict inequality?

• Dotted line

• No line

• Dashed line

• Solid line

What does a non-strict inequality symbol indicate?

• The inequality is greater than

• The inequality is less than

• The inequality excludes equality

• The inequality includes equality

What happens if the inequality was strict instead of non-strict?

• The line would be solid

• The line would be dashed

• The circle would be smaller

• The circle would be larger

What is the purpose of testing a point inside the circle?

• To find the center of the circle

• To determine the radius

• To decide which region to shade

• To check if the circle is correct

Which point is tested to determine the shading region?

• (1, 1)

• (0, 0)

• (3, 3)

• (-3, -3)