Notice that the graph of f(x) is the graph of the function g(x)=|x| stretched horizontally by a factor of 2, reflected over the x-axis, translated 8 units to the left, and 5 units down.
Now, recall that the vertex of |x| is the point (0,0), and it is a fixed point under stretches or reflections over the axis.
Therefore, the vertex of f(x) is the vertex of g(x) translated 8 units to the left, and 5 units down, meaning:
Answer: First option.