Answer
If r is a zero of even multiplicity, then the graph touches the x-axis and turns around. If r is a zero of odd multiplicity, then the graph crosses the x-axis.
Work Step by Step
A function $f\left( x \right)={{\left( x-r \right)}^{k}}$ with r as the zero of the polynomial and the integer k is called the multiplicity of the polynomial. There exists a certain relationship between the multiplicity of a zero and the graph of the polynomial at the point, that is:
In case there is an even multiplicity of a zero of a polynomial, then, the graph touches the x-axis at the point and turns around.
In case if there is an odd multiplicity of a zero of a polynomial, then, the graph of the polynomial touches the x-axis at the point and moves on without returning (that is, it crosses the axis).
