Quadratic functions

Definition: A function of the form
$$y(x)=ax^2+bxy+cy^2 +dx +ey +f,$$
where $a,b,c,d,e$ and $f$ are numbers such that $a, b$ and $c$ are not all simultaneously equal to zero, is called a quadratic function of two variables.

Remark 1: For $a=b=c=0$ this function is linear.

Remark 2: For $a=b=c=d=e=0$ this function is constant.

Example: $z(x,y)=x^2 + y^2 - 1$ is an example of a quadratic function.