The function \( v(x) = |x - 10| \) is in vertex form for an absolute value function, where the vertex occurs at the point where the expression inside the absolute value is equal to zero.
To find the x-coordinate of the vertex, set the inside of the absolute value to zero:
\[ x - 10 = 0 \]
Solving this gives:
\[ x = 10 \]
Thus, the x-coordinate of the vertex is \( 10 \), which represents the length of the paddle board in feet where the variation is centered.
In summary:
The x-coordinate of the vertex of the function is 10, which represents the standard or most popular length of paddle boards in feet.