This is the concept of algebra, a function is defined as a relationship whereby each input has one and only one single output.
In our expression;
y=-3x^2-7x-6
this can be written as:
f(x)=-3x^2-7x-6
such that, given x=0,1,2,....
f(0)=-6,
f(1)=-16
f(2)=-32
This implies that y is a function of x.