The function f(x) = x² - 8x + 19 is equivalent to which of the following, where the minimum value of f is visible directly from the…

Complete the square. Half of $-8$ is $-4$, and $(-4)^2 = 16$. Write $x^2 - 8x + 19 = (x^2 - 8x + 16) + 3 = (x - 4)^2 + 3$, choice C. In this form the vertex is $(4, 3)$ and the minimum value is 3, since a square is never negative. Choice A keeps 19 without adjusting for the 16 that was added inside the square. Choice B uses $(x-8)^2$, forgetting to halve the coefficient. Choice D has the correct square but subtracts 3, which comes from a sign error when moving 16 across: $19 - 16 = +3$, not $-3$.