You are watching: A quadratic polynomial has a degree of 2

But the listed below polynomial is also of degree 2 and also non quadratic:

xy + x + y

So, why perform we say, polynomial of level 2 is a quadratic function?

We say it since of conventions. It makes sense.

I think the best reason why is that whether a duty on the airplane is quadratic shouldn"t count on exactly which coordinate axes we impose ~ above the plane. Because that instance, if ns didn"t choose your $xy$-axes, and instead wanted $uv$-axes $45^circ$ to yours (say my allude $(1,0)$ is at your $(1,1)$ and also my allude $(0,1)$ is at your $(-1,1)$), climate my expression for the *same function* would be$$frac14u^2-frac14v^2 + u$$which clearly has quadratic terms.

$xy+x+y =0$ (I added the = 0 to do your question complete) is no of degree two for x.

Rearranging: $y=frac-xx+1$

Thus that is not quadratic.

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Every non-negative multivariate polynomial has even degree and also the highest degree term has positive coefficient?

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