Which function has a vertex at (2, –9)?

A quadratic in factored form has its axis of symmetry halfway between its roots. For f(x) = (x – 5)(x + 1), the roots are 5 and –1, so the axis is x = (5 + (–1))/2 = 2. Substituting x = 2 gives f(2) = (2 – 5)(2 + 1) = (–3)(3) = –9, so its vertex is (2, –9). The correct choice is C, f(x) = (x – 5)(x + 1).

AI-written and checked against the verified answer.