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

Explanation:

Step1: Recall vertex - form of a quadratic function

The vertex - form of a quadratic function is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola and the axis of symmetry is given by the equation $x = h$.

Step2: Identify the value of h in the given function

For the function $f(x)=(x - 2)^2+1$, comparing it with $y=a(x - h)^2+k$, we have $h = 2$ and $k = 1$. So the axis of symmetry is the vertical line $x=2$.

Answer:

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