Graphing and Analyzing Inequalities

The video tutorial explains how to graph the solution to a system of inequalities. It covers graphing a quadratic inequality, y < x^2 - 6, using a dashed parabola and determining the shaded region. It also explains graphing a linear inequality, y >= -1/4x + 3, using a solid line and identifying the shaded region. The solution to the system is the double shaded region, which is unbounded.

What is the solution to a system of inequalities?

• The region below both graphs

• The region where the graphs do not overlap

• The region above both graphs

• The region where the graphs overlap

How is the graph of y < x^2 - 6 represented?

• As a solid line

• As a dashed line

• As a dashed parabola

• As a solid parabola

What is the vertex of the parabola y = x^2 - 6?

• (0, 0)

• (0, -6)

• (6, 0)

• (-6, 0)

Which region is shaded for the inequality y < x^2 - 6?

• Above the parabola

• Below the parabola

• Inside the parabola

• On the parabola

What test point is used to verify the shading of the quadratic inequality?

• (-1, -1)

• (0, 0)

• (2, 2)

• (1, 1)

How is the graph of y >= -1/4x + 3 represented?

• As a solid line

• As a dashed line

• As a solid parabola

• As a dashed parabola

What is the slope of the line y = -1/4x + 3?

• -1/4

• -4

• 4

• 1/4

Which region is shaded for the inequality y >= -1/4x + 3?

• Above the line

• Inside the parabola

• On the line

• Below the line

What is the solution to the system of inequalities?

• The region on both graphs

• The double shaded region

• The region below both graphs

• The region above both graphs

Does the solution to the system include points on the parabola?

• Yes, because the parabola is solid

• No, because the parabola is dashed

• No, because the parabola is solid

• Yes, because the parabola is dashed