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A polynomial graph touches the x-axis at a zero and turns back. What does that show?
AThat zero has even multiplicity
BThat zero has odd multiplicity
CThat zero is not a real number
DThat zero raises the degree by 1
Answer & Solution
Correct answer: A. That zero has even multiplicity
1. Behaviour at an x-intercept is set by the power on the matching factor.
2. An even power makes the graph touch the axis and bounce back.
3. An odd power makes the graph pass through the axis.
4. So a touch and turn marks a zero of even multiplicity.
_Source: OpenStax Precalculus (CC BY 4.0), section 3.4 Graphs of Polynomial Functions_