Which graph shows the axis of symmetry for the function f(x) = (x-2)^2 + 1?

Step 1: Define the Problem

Identify the axis of symmetry for the quadratic function $f(x) = (x-2)^2 + 1$.

Step 2: Break Down the Problem

1. Recognize the standard form of a quadratic function: $f(x) = a(x-h)^2 + k$.
2. Identify the vertex of the function, which is at the point $(h, k)$.

Step 3: Apply Relevant Concepts

• The axis of symmetry for a quadratic function in the form $f(x) = a(x-h)^2 + k$ is the vertical line $x = h$.

Step 4: Analysis, Verify and Summarize

• For the function $f(x) = (x-2)^2 + 1$, the vertex form is already given, where $h = 2$ and $k = 1$.
• Therefore, the axis of symmetry is the line $x = 2$.

Final Answer

The graph that shows the axis of symmetry for the function $f(x) = (x-2)^2 + 1$ is the one with the vertical line $x = 2$.