Video Transcript
The given graph is of a polynomial
𝑓. What is the degree of 𝑓? Is it one, two, three, four, or
five?
Remember, a polynomial of degree or
order 𝑛 can have up to 𝑛 minus one turning points. In other words, if we can find the
degree of our polynomial, we can know it can have up to one less than this turning
points. So, let’s count the turning points
of our graph. We see the graph changes direction
here and here. But what’s happening over here? Well, the graph doesn’t actually
appear to fully change direction, and that’s because it doesn’t. This is, in fact, a point of
inflection. It’s a point where the concavity of
the graph changes.
Now, another fact is that a
polynomial of degree 𝑛 can have up to 𝑛 minus two inflection points. And we can think of the inflection
points a little bit like the graph changing direction really quickly twice in a
short space of time. We can consider this as two turning
points. This means we have a total of
four. And so, the degree of our
polynomial must be five.
