The function f(x) = x² - 4x - 5 can be written in vertex form as f(x) = (x-h)² + k. What is the value of h + k?

Complete the square. Half of $-4$ is $-2$, and $(-2)^2 = 4$, so $x^2 - 4x - 5 = (x^2 - 4x + 4) - 4 - 5 = (x - 2)^2 - 9$. In vertex form $(x - h)^2 + k$, we have $h = 2$ and $k = -9$, so $h + k = -7$. Check: the vertex is $(2, -9)$, and $f(2) = 4 - 8 - 5 = -9$. A common wrong answer is $-11$, from taking $h = -2$ (misreading the sign inside the parentheses). Another is $-9$, which is only $k$. Remember the form is $(x - h)$.