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Sagot :

The parent function f(x) = x² is a parabola and its vertex is located at the origin (0,0). we can identify what type of transformation and its rule was applied to this parabola by identifying the new location of the vertex.

In this case, we go from f(x) = x² to f(x) = (x - 3)² + 2, that is we are translating the parabola 3 units right (we are subtracting 3 from x) and the parabola is translated 2 units up (2 is being added outside the parenthesis), when we do that the vertex of the parabola should also move two units up and 3 units right, as you go two units up from (0,0) you get (0,2) as you move three units right from (0,2) you get (3,2).

Then, the vertex of the parabola after the translation should be (3, 2). The only graph with a vertex located at (3, 2) is option C, then option C is the correct answer.

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