The function you are referring to is f(x) = |x – 2| + 4, which is an absolute value function. To find the vertex of this function, we first need to understand the general form of an absolute value function, which is given by f(x) = |x – h| + k, where (h, k) is the vertex.
In your equation, we can identify the values of h and k:
- h = 2 (the value inside the absolute value)
- k = 4 (the constant added outside the absolute value)
Therefore, the vertex of the function f(x) = |x – 2| + 4 is located at the point (2, 4).
This means that at x = 2, the function reaches its minimum value of 4, and from this point, the function will increase as you move away from 2 in both directions along the x-axis. The absolute value function creates a V-shape, which opens upwards, confirming that (2, 4) is indeed the lowest point or vertex of the graph.
So in summary, the vertex of the function f(x) = |x – 2| + 4 is (2, 4).