What does the Wavy Line Method help to determine in the context of inequalities?

The Wavy Line Method is a graphical technique used to determine the range of values that satisfy a given inequality, particularly in the context of quadratic inequalities. When applied, it involves sketching a number line and marking the roots of the quadratic equation derived from the inequality. The regions of the number line are then tested to find out where the inequality holds true.

In the context of quadratic inequalities, once the roots are established, the Wavy Line Method helps identify intervals on the number line where the quadratic expression is either greater than or less than zero. By following the pattern established by the above and below the x-axis, one can easily deduce the range of values for which the inequality is satisfied. This makes it a powerful tool for determining the valid solutions or range of a quadratic inequality.

The focus on establishing these intervals directly relates to identifying the range rather than finding a specific maximum value, intersection points of equations, or calculating areas of geometric shapes, which are not objectives of this method.