When the graph of a polynomial touches the x-axis and then turns back, it indicates that the zero at that point has an even multiplicity. This is because even multiplicities do not cross the x-axis but instead result in the graph intersecting tangentially.
Among the options provided:
- 1: This is an odd multiplicity and would cross the x-axis.
- 3: This is also an odd multiplicity and would cross the x-axis.
- 2: This is an even multiplicity, which allows the graph to touch the x-axis and turn back.
- 0: This concept does not apply to multiplicity in the context of zeros.
Thus, the only option from the list that could represent the multiplicity of a zero where the graph touches the x-axis and turns back is:
2.