Definition

A function defined by f(x) = ax² + bx + c, where a, b, c∈ℝ and a ≠ 0, is called a quadratic function

• a is called the leading coefficient, and c is called the constant term.
• The domain of a quadratic function is the set of all real numbers.

Example

f (x) = 2x² - 3x + 2 is a quadratic function with a = 2, b = -3, and c = 2.

Note: Any function that can be reduced to the form f (x) = ax² + bx + c is a quadratic function.

Example

(a) f(x) = (x – 3)² +5 can be expressed as f (x) = x² – 6x + 14
So, f(x) = (x – 3)² +5 is a quadratic function with a = 1, b = -6, and c =14.
(b) f(x) = (x – 2)(x + 2) can be expressed as f (x) = x² – 4.
So, f(x) = (x – 2)(x + 2) is a quadratic function with a = 1, b = 0, and c = –4.