Visualizing Quadratic Inequalities on a Number Line
Your Task
Identifying the Critical Points
At which x-values does the graph touch or cross the x-axis? How can you mark these points on the number line?
Identifying the Critical Points
How do these points divide the number line into different regions (or intervals)?
Determining the Solution Set on the Number Line
How can you determine which regions of the number line should be shaded based on where the graph is above or below the x-axis?
Determining the Solution Set on the Number Line
When should you use open circles (for > or <) or closed circles (for ≥ or ≤ ) at these points on the number line?
Expressing the Solution
How can you express the shaded regions on the number line using inequality notation, interval notation, or set notation?
Expressing the Solution
How would the number line change if the quadratic inequality has exactly one solution (the graph just touches the x-axis at a single point)?
How do these points divide the number line into different regions (or intervals)?