by wikipedia:In algebra, a quadratic function, a quadratic polynomial, a polynomial of level 2, or merely a quadratic, is a polynomial function in one or more variables in i beg your pardon the highest-degree ax is the the second degree.

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

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

xy + x + y

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


We speak it because of conventions. It makes sense.

I think the greatest reason why is that whether a role on the airplane is quadratic shouldn"t rely on precisely which name: coordinates axes we impose ~ above the plane. Because that instance, if i didn"t like your $xy$-axes, and instead want $uv$-axes $45^circ$ to yours (say my allude $(1,0)$ is at your $(1,1)$ and my suggest $(0,1)$ is at her $(-1,1)$), climate my expression for the same function would be$$frac14u^2-frac14v^2 + u$$which clearly has quadratic terms.


$xy+x+y =0$ (I included the = 0 to do your question complete) is not of level two because that x.

Rearranging: $y=frac-xx+1$

Thus it is no quadratic.


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