Quadratic Inequalities and Parabolas

The video tutorial explains how to graph solutions to a system of quadratic inequalities. It covers solving each inequality, graphing the corresponding parabolas, and identifying the solution region. The first inequality results in a solid parabola, while the second results in a dashed parabola. The tutorial details finding the axis of symmetry, vertex, and intercepts for each parabola, and emphasizes shading the correct regions to represent solutions. The final solution is the double-shaded region where both inequalities overlap.

What type of parabola is used when the inequality is 'greater than or equal to'?

• Solid parabola

• Dashed parabola

• Dotted parabola

• No parabola

For the first quadratic inequality, what is the equation of the axis of symmetry?

• x = 1

• x = 2

• x = -1

• x = -2

What is the vertex of the first quadratic function y = x^2 + 2x - 8?

• (-1, -9)

• (1, 9)

• (1, -9)

• (-1, 9)

Which region is shaded for the inequality y > x^2 + 2x - 8?

• Below the parabola

• Above the parabola

• Outside the parabola

• No shading

What is the axis of symmetry for the second quadratic inequality y = -x^2 - 4x?

• x = -2

• x = 4

• x = -4

• x = 2

What is the vertex of the second quadratic function y = -x^2 - 4x?

• (4, -2)

• (-4, 2)

• (2, -4)

• (-2, 4)

For the inequality y < -x^2 - 4x, where is the shading done?

• Above the parabola

• Outside the parabola

• No shading

• Below the parabola

Which point is both an x-intercept and a y-intercept for the second quadratic function?

• (4, 0)

• (-4, 0)

• (0, -4)

• (0, 0)

What is the solution to the system of quadratic inequalities?

• The double shaded region

• The region above both parabolas

• The region below both parabolas

• The region outside both parabolas

Which part of the graph is not included in the solution to the system?

• The solid parabola

• The dashed parabola

• Neither parabola

• Both parabolas