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

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

Step 3: Apply Relevant Concepts

For the given function $f(x) = (x - 2)^2 + 1$, compare it to the standard form $(x - h)^2 + k$:

• Here, $h = 2$.

Step 4: Analysis, Verify and Summarize

The axis of symmetry is a vertical line that passes through $x = h$. Therefore, for this function, the axis of symmetry is $x = 2$.

Final Answer

The axis of symmetry for the function $f(x) = (x - 2)^2 + 1$ is the line $x = 2$.