Turns, Ends, and the Bend

You'll learnto read a polynomial's landmarks: where it crosses, where it turns, and where it changes its bend.

A polynomial's landmarks come in three flavours and two strengths. Between any two distinct zeros the graph is forced to turn; the degree decides whether any of those turns is global; and the bend can flip somewhere the function never turns at all.

8 STEPS · 6 QUICK CHECKS · LOCAL vs GLOBAL · FORCED TURNS · INFLECTION · v2

local ranks a neighbourhood; global ranks the whole domain

Before you start

What you're looking at

A single polynomial graph with its zeros, a turning point, and an inflection point marked.

The question

At each marked spot, is the graph crossing, turning, or flipping its concavity?

Watch for

The difference between a local landmark (judged against nearby points) and a global one (judged against the whole graph).

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