General Form of Quadratic Function

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.

  1. f ( x ) = ( 5 x 3 ) ( 3 x + 8 )
  2. f ( x ) = 2 ( 3 x + 8 )
  3. f ( x ) = 5 2 x 2
Answer:
(a)
  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

Quadratic function
(b)
f ( x ) = 2 ( 3 x + 8 ) f ( x ) = 6 x + 16
Not quadratic function

(c) Not quadratic function

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