Graphing Inequalities and Parabolas

The video tutorial explains how to graph the solution to a system of inequalities. It covers graphing a quadratic inequality y ≥ x² - 4 and a linear inequality y < -1/2x + 3. The tutorial demonstrates plotting points, identifying the axis of symmetry, and shading the appropriate regions. The solution to the system is the double shaded region, which includes points that satisfy both inequalities.

What is the solution to a system of inequalities?

• The union of the graphs of the inequalities

• The area below the graphs of the inequalities

• The intersection of the graphs of the inequalities

• The area above the graphs of the inequalities

What is the vertex of the parabola y = x² - 4?

• (0, 4)

• (0, -4)

• (4, 0)

• (-4, 0)

How do you determine the direction of shading for the inequality y ≥ x² - 4?

• Shade to the right of the parabola

• Shade to the left of the parabola

• Shade above the parabola

• Shade below the parabola

Which test point is used to verify the shading for the inequality y ≥ x² - 4?

• (1, 1)

• (0, 0)

• (-1, -1)

• (2, 2)

What is the slope of the line y = -1/2x + 3?

• -2

• 1/2

• -1/2

• 2

How is the line y = -1/2x + 3 graphed?

• As a dotted line

• As a solid line

• As a bold line

• As a dashed line

Where do you shade for the inequality y < -1/2x + 3?

• To the right of the line

• Below the line

• Above the line

• To the left of the line

What is the solution to the system of inequalities?

• The region above both graphs

• The region below both graphs

• The double shaded region

• The region outside both graphs

Which points are included in the solution to the system of inequalities?

• Points neither on the line nor parabola

• Points only on the line

• Points on the line and parabola

• Points only on the parabola

What does the double shaded region represent in the graph of a system of inequalities?

• The area that satisfies neither inequality

• The area that satisfies only one inequality

• The area that satisfies the opposite of both inequalities

• The area that satisfies both inequalities