The vertex of the absolute value function f(x) = |x – 2| + 4 can be determined by analyzing the expression inside the absolute value and the constant added to it. In this case, the function is defined as f(x) = |x – 2| + 4.
The expression inside the absolute value, x – 2, indicates a horizontal shift. The absolute value function |x – a| has its vertex at the point (a, 0). Therefore, for our function, the x-coordinate of the vertex is 2.
Next, we observe that the +4 shifts the entire graph upward by 4 units. Thus, the y-coordinate of the vertex becomes 0 + 4 = 4.
Putting it all together, the vertex of the function f(x) = |x – 2| + 4 is located at the point (2, 4). This point represents the minimum value of the function, as the graph of an absolute value function opens upwards.