What is a quadratic function? (brief explanation)

The quadratic function has the form:

where a, b, and c are numerical constants and c is not equal to zero.

Note that if c were zero, the function would be linear.

An advantage of this notation is that it can easily be generalized by adding more terms.  We could for example write equations such as

y  =    a  +  bx  +  cx2  + dx3

y  =    a  +  bx  +  cx2  + dx3  + ex4