Short Answer 
The function f(x)=(x-2)^2+1 represents a parabola with its vertex at x=2. Consequently, the axis of symmetry is the vertical line x=2, which divides the parabola into two equal halves.
Step 1: Understand the Given Function
The function we are analyzing is f(x)=(x-2)^2+1, which represents a parabola. To identify the axis of symmetry, we need to recognize that this is a vertical line that divides the parabola into two equal halves. The axis of symmetry intersects the parabola at its vertex.
Step 2: Find the Vertex of the Parabola
To locate the vertex, we will convert the function into the standard quadratic form (ax^2 + bx + c). Therefore, we rewrite the function as f(x)=x^2-4x+5. Now, we can apply the vertex formula x = -b/(2a), where a = 1 and b = -4.
- Substitute a and b into the formula: x = -(-4)/(2*1)
- This simplifies to x = 4/2.
- Thus, x = 2 is the x-coordinate of the vertex.
Step 3: Determine the Axis of Symmetry
Now that we have found the vertex at x = 2, the axis of symmetry is the vertical line that passes through this point. Therefore, the axis of symmetry for the function f(x) is located at x = 2. If presented with graph options, Graph B will correctly display this axis of symmetry.