What is the vertex of the absolute value function defined by ƒ(x) = |x + 5| + 7?

To answer this, you need to know the general form of an absolute value function. the equation for this is f(x) = a|x - h| + k, and in this equation, the vertex is (h, k).

with that information, you can see that your vertex will be (-5, 7). you must take the negative for 5 because the general equation states that your h value is usually subtracted from x. to check your vertex, try plugging it into your general equation:
f(x) = a|x - (-5)| + 7
f(x) = a|x + 5| + 7 ... you see that this matches your given equation. this last part here was just to show why your 5 must be negative; your answer is bolded.