The function \( f(x) = (x - 1)^2 + 7 \) is in vertex form, which is given by \( f(x) = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.
From the given function:
- \( h = 1 \)
- \( k = 7 \)
Thus, the vertex is \( (1, 7) \).
The axis of symmetry for a parabola in vertex form is given by the line \( x = h \). Therefore, the axis of symmetry here is:
\[ x = 1 \]
In conclusion, we have:
- The vertex is \( (1, 7) \).
- The axis of symmetry is \( x = 1 \).