Question

The most popular lengths of paddle boards can be written by the function v(x)=|x−10| where x is the length of the paddle board in feet, and v represents a variation of 4 feet.
Complete the statement.

(4 points)
The x coordinate of the vertex of the function is
which represents
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Answer 1

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.**