1. The problem states that the function describing the lengths of paddle boards is $$v(x) = |x - 10|$$ where $x$ is the length in feet and $v$ is the variation. 2. The vertex of an absolute value function $$v(x) = |x - h|$$ is at $$x = h$$. Here, the vertex is at $$x = 10$$. 3. The vertex represents the point where the variation $$v(x)$$ is zero, meaning the length $$x = 10$$ has no variation from itself. 4. Since $$v(x)$$ measures variation from 10, the vertex at 10 represents the average length of the paddle board, as lengths vary around this value. 5. Therefore, the vertex of the function is 10 which represents the average length of a paddle board. Final answer: The vertex of the function is 10 which represents the average length of a paddle board.