What allows the Wavy Line Method to quickly demonstrate the range of a quadratic inequality?

The Wavy Line Method provides a visual representation that effectively conveys the behavior of a quadratic inequality. By drawing a wavy line on a number line, the method showcases the intervals where the quadratic function is either above or below the x-axis, indicating the nature of the inequality.

This visual approach allows for a quick and intuitive grasp of the solution. The ups and downs of the wavy line correspond to the sign changes of the quadratic expression, facilitating a clear understanding of where the quadratic is positive or negative. Furthermore, it helps identify critical points, which are where the inequality changes from true to false or vice versa.

In contrast to algebraic computation, graph plotting, or numerical analysis, which may involve more complex calculations or require additional steps to interpret data, the strength of the Wavy Line Method lies in its straightforward, visual interpretation of quadratic inequalities. This makes it an efficient tool for solving and analyzing the range of these inequalities in a clear and immediate manner.