Quadratic equations are characterized by having a degree equal to two, and their graphical representation forms a parabola.
For the given function: f(x) = (x – 2)2 + 1, we can see that it is in vertex form, with the vertex at (2, 1).
The graph of the function f(x) = (x – 2)22 + 1 is displayed above.
Upon examining the graph, it’s evident that the curve of the equation is an upward-facing parabola with its vertex located at (2, 1).
Furthermore, because the curve does not intersect the x-axis, it indicates that f(x) has no real roots.
In conclusion, the graph that illustrates the axis of symmetry for the function f(x) is the parabola with its vertex at (2, 1).