Answer:
(d) g(x) = (x – 5)² + 2
Step-by-step explanation:
You want the equation of the parabola f(x) = x² after its vertex has been translated to (5, 2).
Translation of function f(x) by (h, k) makes the function be ...
g(x) = f(x -h) +k
When the vertex of f(x) = x² has been translated by (5, 2), it becomes ...
g(x) = f(x -5) +2
g(x) = (x -5)² +2 . . . . . matches choice D
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Additional comment
Translation by (h, k) moves the graph h units to the right and k units up. We only need to know how one point is translated in order to know what the translated function is. It is convenient to use the vertex as that reference point.