Is the product of two linear functions always a quadratic function?

Yes, the product of two linear functions is always a quadratic function. A linear function can be expressed in the form ( f(x) = ax + b ) and ( g(x) = cx + d ). When you multiply these two functions, ( f(x) \cdot g(x) = (ax + b)(cx + d) ), the result is a polynomial of degree 2, which is the definition of a quadratic function.