the general formula for an absolute value function is f(x) = a|x - h| + k. in this formula, your vertex is (h, k).
all you have to do to answer this question is view (h, k) in your formula f(x) = |x - 7| + 1
7 is in the place of h and 1 is in the place of k. this makes your vertex (7, 1).
