Question

what is the domain of all quadratic functions?

\\(x > 0\\)
\\(x < 0\\)
\\(x < \infty\\)
all real numbers

Explanation:

Define a quadratic function

$$ f(x) = ax^2 + bx + c, \quad a eq 0 $$

Determine domain restrictions

$$ \text{No division by zero, no square roots of negative numbers.} $$

Identify the domain

$$ x \in (-\infty, \infty) \implies \text{All Real Numbers} $$

Answer:

• (A) \(x > 0\)
• (B) \(x < 0\)
• (C) \(x < \infty\)
• (D) All Real Numbers (Correct answer)