Graphing Inequalities and Parabolas

The video tutorial explains how to graph a system of inequalities on a coordinate plane. It covers graphing a quadratic inequality, y < -x^2 + 4, using a dashed parabola and shading the region inside. Then, it demonstrates graphing a linear inequality, y >= x + 5, with a solid line and shading above it. The tutorial concludes by showing that there is no double shaded region, indicating no solution to the system of inequalities.

What is the solution to a system of inequalities?

• The entire coordinate plane

• The region where only one inequality is satisfied

• The region where both inequalities are satisfied

• The region where no inequalities are satisfied

What type of line is used to graph the inequality y < -x^2 + 4?

• Dashed line

• Dotted line

• Solid line

• Bold line

Where is the vertex of the parabola y = -x^2 + 4 located?

• (4, 4)

• (0, 4)

• (4, 0)

• (0, 0)

How do you determine the direction of shading for the inequality y < -x^2 + 4?

• Shade to the right of the parabola

• Shade to the left of the parabola

• Shade below the parabola

• Shade above the parabola

What is the significance of the axis of symmetry in graphing a parabola?

• It determines the slope of the parabola

• It is the lowest point of the parabola

• It helps in finding corresponding points

• It is the highest point of the parabola

What is the slope of the line y = x + 5?

• 5

• -1

• 1

• 0

What type of line is used to graph the inequality y ≥ x + 5?

• Bold line

• Dotted line

• Dashed line

• Solid line

How do you determine the direction of shading for the inequality y ≥ x + 5?

• Shade above the line

• Shade below the line

• Shade to the left of the line

• Shade to the right of the line

What is the result when there is no double shaded region in a system of inequalities?

• There is a unique solution

• There are infinite solutions

• There is no solution

• The solution is the entire plane

What does it mean if a test point satisfies an inequality?

• The point is irrelevant

• The point is outside the solution region

• The point is inside the solution region

• The point is on the boundary