Understanding the Wavy Curve Method for Solving Polynomial Inequalities

[Smarty7]

It is said to be a method to solve inequalities in the form of
\frac{P(x)}{Q(y)} \leq 0

\frac{P(x)}{Q(y)} \geq 0

P(x) and Q(y) are polynomials.

 

[Gib Z]

It's basically to roughly sketch P and Q as graphs on two separate axis, from which we can observe which intervals they are negative or positive. We can combine the information of both to determine when the ratios are negative or positive.

You should have learned how to roughly sketch polynomials in calculus. For this purpose, you only need to find the roots and how the graph passes through them (bounce back off, or pass through the axis), and not the values of extreme values or where exactly they occur. The quick rule is that if the root has even multiplicity, the curve bounces back off the axis, while roots with odd multiplicity pass straight through. You can use Calculus to check that if you want.