Understanding Quadratic Inequalities Graphically

This video tutorial explains how to solve quadratic inequalities graphically. It covers the concepts of f(x) being greater than, less than, or equal to zero, and how these relate to the graph's position relative to the x-axis. The tutorial provides step-by-step solutions for different inequalities, using interval notation and number line representations to illustrate the solutions.

What does it mean when f(x) is greater than zero in terms of the graph?

• The graph is below the x-axis.

• The graph is on the x-axis.

• The graph is above the x-axis.

• The graph intersects the y-axis.

When solving f(x) > 0, which of the following is true about the endpoints of the interval?

• Only the right endpoint is included.

• Endpoints are included.

• Endpoints are excluded.

• Only the left endpoint is included.

How is the solution for f(x) > 0 expressed in interval notation?

• [3, 4)

• [-3, 4]

• (-3, 4)

• (-3, 4]

What additional part of the graph is included when solving f(x) ≥ 0 compared to f(x) > 0?

• The graph below the x-axis.

• The graph on the x-axis.

• The graph on the y-axis.

• The graph above the y-axis.

In interval notation, how is the solution for f(x) ≥ 0 expressed?

• [0, 6)

• (0, 6)

• (-∞, 0] ∪ [6, ∞)

• [0, 6]

When solving f(x) ≤ 0, which intervals are included in the solution?

• Intervals where the graph is above the y-axis.

• Intervals where the graph is below or on the x-axis.

• Intervals where the graph is on the y-axis.

• Intervals where the graph is above the x-axis.

How is the solution for f(x) ≤ 0 expressed in interval notation?

• [2, 4)

• (-2, 4]

• [-2, 4]

• (-2, 4)

What is excluded when solving f(x) < 0?

• The graph below the y-axis.

• The graph above the x-axis.

• The x-intercepts.

• The graph on the y-axis.

In interval notation, how is the solution for f(x) < 0 expressed?

• (-3, 4]

• (-∞, -3) ∪ (4, ∞)

• (-3, 4)

• [3, 4)

What does it mean when f(x) is less than zero in terms of the graph?

• The graph is on the x-axis.

• The graph is below the x-axis.

• The graph is above the x-axis.

• The graph intersects the y-axis.