Q. 43 - Precalculus Enhanced with Graphing Utilities

Question

Explain the circumstances under which the x-intercepts of the graph of a quadratic function are included in the solution set of a quadratic inequality.

Step-by-Step Solution

Answer

The inequalities of the type "less than equal to"  and "greater than equal to " have the x-intercept.  as a solution.

Step 1. Given information

The x-intercepts are included in the solution set.

Step 2. Find the reason

• The inequality of the type $f\left(x\right)\le 0$ requires the solution where the function lies on the horizontal axis or below it.
• Similarly, the inequality of the type $f\left(x\right)\ge 0$requires the solution where the function lies on the horizontal axis or above it.
• The point that lie on the horizontal axis is the x-intercept.
• So, the inequalities of the type "less than equal to"  and "greater than equal to " have the x-intercept.  as a solution.