A polynomial graph touches the x-axis at a zero and turns back. What d…

Question

A polynomial graph touches the x-axis at a zero and turns back. What does that show?

Accepted 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_

Answer

That zero has odd multiplicity

Answer

That zero is not a real number

Answer

That zero raises the degree by 1

A polynomial graph touches the x-axis at a zero and turns back. What does that show?

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