Suppose $f$ is a real valued function with domain a subset of
real numbers, $D$.

Definition: $f$ is a **quadratic function**
if **there a numbers $A$, $B$, and $C$ with $A \ne 0$ so
that for any $x \in D$, $f(x) = Ax^2 + Bx +C$**

**Comment: **The letters ** $A$, $B$, and $C$** have
been used to conform with the naming of these coefficients in
quadratic equations, but there are alternatives. Here is an
alternative:

__$f$__ is a quadratic function if there a numbers**
$a_2$, $a_1$, and $a_0$** with $a_2 \ne 0$ so that for any
$x \in D$, **$f(x) =a_2x^2+ a_1 x +a_0$**.

The number **$A$ **is sometimes referred to as the
"leading coefficient " of the quadratic function.

The number **$B$ **is sometimes referred to as the
"linear coefficient " of the quadratic function.

The number** $C$** is sometimes referred to as "the $y$-
intercept," "the initial value," or the "constant " of the quadratic
function.