**General Form of Quadratic Function**

General form of a quadratic function is
$f(x)=a{x}^{2}+bx+c$
where a, b, and c are constants and a ≠ 0, and x as a variable.

Example:

Example:

Determine which of the following is a quadratic function.

- $f(x)=(5x-3)(3x+8)$
- $f(x)=2(3x+8)$
- $f(x)=\frac{5}{2{x}^{2}}$

**Answer**:

(a)

$\begin{array}{l}f(x)=(5x-3)(3x+8)\\ f(x)=15{x}^{2}+40x-9x-24\\ f(x)=15{x}^{2}+31x-24\end{array}$

Quadratic function

(b)

$\begin{array}{l}f(x)=2(3x+8)\\ f(x)=6x+16\end{array}$

Not quadratic function

(c) Not quadratic function