Graphing Nonlinear Inequalities

The video tutorial explains how to graph a nonlinear inequality, specifically focusing on the inequality y ≤ x² - 2. It covers the process of treating the inequality as an equation to graph it, deciding whether the graph should be solid or dashed, and determining which region to shade. The tutorial uses a parabola as an example, demonstrating how to apply transformations and test points to identify the correct region to shade.

What is the main difference between graphing linear and nonlinear inequalities?

• Nonlinear inequalities do not require a graph.

• Linear inequalities require shading.

• Nonlinear inequalities involve curves instead of straight lines.

• Nonlinear inequalities use dashed lines.

When graphing a nonlinear inequality, what is the first step?

• Solve the inequality algebraically.

• Shade the region immediately.

• Choose a point to test.

• Pretend the inequality is an equation and graph it.

What is the inequality being graphed in the video?

• y ≥ x^2 + 2

• y > x^2 + 2

• y < x^2 - 2

• y ≤ x^2 - 2

What shape does the graph of y ≤ x^2 - 2 take?

• An ellipse

• A parabola

• A circle

• A straight line

How is the parabola y = x^2 - 2 transformed?

• Shifted left by 2 units

• Shifted down by 2 units

• Shifted right by 2 units

• Shifted up by 2 units

Why is the parabola solid in the graph of y ≤ x^2 - 2?

• Because it is a dashed line

• Because it is not an inequality

• Because it includes the boundary

• Because it is a strict inequality

Which point is used to test the inequality in the video?

• (2, 2)

• (1, 1)

• (0, 0)

• (-1, -1)

What is the result of plugging the point (0, 0) into the inequality y ≤ x^2 - 2?

• 0 ≤ -2, which is true

• 0 ≤ -2, which is false

• 0 ≤ 2, which is true

• 0 ≤ 2, which is false

What does the result of the test point (0, 0) indicate about the shading?

• Shade both regions

• Shade the region containing (0, 0)

• Shade the opposite region

• Do not shade any region

What is the final step in graphing the inequality?

• Check another point

• Erase the graph

• Shade the correct region

• Change the inequality to an equation