(A) General Form of Quadratic Function

Posted on April 18, 2020 by user

3.1 General Form of Quadratic Function

General form of a quadratic function is

$f (x) = a x^{2} + b x + c$ where a, b, and c are constants and a ≠ 0, and x as a variable.

Example:
Determine which of the following is a quadratic function.

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

Answer:
(a)

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

(b)

$\begin{array}{l} f (x) = 2 (3 x + 8) \\ f (x) = 6 x + 16 \end{array}$
Not quadratic function

(c) Not quadratic function