The graph of f (x) = x2 is translated to form g (x) = (x - 5) 2 + 1. Which graph represents g (x) ?

The graph would be translated 5 units right and 1 unit up, giving an upward facing parabola with a vertex at (5, 1).

Explanation:

Since 5 was subtracted from x before it was squared, this means a horizontal translation 5 units. Since it was subtracted, this means it was translated right 5 units.

The 1 added at the end means it was translated 1 unit up as well.

This is in vertex form, y=a (x-h) ^2 + k, where (h, k) is the vertex; h corresponds with 5 and k corresponds with 1, so the vertex is at (5, 1).