What is the vertex of the graph of \( g(x)=|x-8|+6 \) ? \( (6,8) \) \( (8,6) \) \( (6,-8) \) \( (-8,6) \)

The vertex of the graph of \( g(x) = |x-8| + 6 \) occurs at the point where the expression inside the absolute value equals zero. This happens when \( x = 8 \). Substituting \( x = 8 \) back into the function gives \( g(8) = |8 - 8| + 6 = 0 + 6 = 6 \). Therefore, the vertex is at the coordinates \( (8, 6) \). To help visualize this, remember that the graph of \( g(x) \) is a V-shape centered around the vertex. The "V" opens upwards and reaches its minimum value at the vertex. This means that every point on the graph to the left and right of the vertex increases in value, making the vertex the "lowest" point on the graph.