The graphs of polynomials show where their roots, or zeros, are located. These roots are the points on the $x$-axis where the graph meets or crosses it.

• Degree and Roots: A polynomial with a degree of $n$ can have up to $n$ roots, counting how many times each root appears.

• Real Roots: When you look at how many times a polynomial touches or crosses the $x$-axis, it tells you how many real roots there are.

• Behavior at Roots:

  • If a root has an even multiplicity, the graph will only touch the $x$-axis but won't cross it.
  • If a root has an odd multiplicity, the graph will cross the $x$-axis.

So, by understanding how polynomials and their graphs are connected, you can better find their roots.