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What kind of transformation converts the graph of f(x)=9(x−6)2f(x) = 9(x - 6)^2 into the graph of g(x)=9(x−3)2g(x) = 9(x - 3)^2?\newlineChoices:\newline(A) translation 33 units right\newline(B) translation 33 units left\newline(C) translation 33 units down\newline(D) translation 33 units up

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Q. What kind of transformation converts the graph of f(x)=9(x−6)2f(x) = 9(x - 6)^2 into the graph of g(x)=9(x−3)2g(x) = 9(x - 3)^2?\newlineChoices:\newline(A) translation 33 units right\newline(B) translation 33 units left\newline(C) translation 33 units down\newline(D) translation 33 units up
  1. Find Vertex of f(x)f(x): Find the vertex of f(x)f(x).f(x)=9(x−6)2f(x) = 9(x - 6)^2 has a vertex at (6,0)(6, 0).
  2. Find Vertex of g(x)g(x): Find the vertex of g(x)g(x).g(x)=9(x−3)2g(x) = 9(x - 3)^2 has a vertex at (3,0)(3, 0).
  3. Compare Vertices of f(x)f(x) and g(x)g(x): Compare the vertices of f(x)f(x) and g(x)g(x). Vertex of f(x)f(x) is (6,0)(6, 0) and vertex of g(x)g(x) is (3,0)(3, 0).
  4. Determine Shift Direction: Determine the direction of the shift. The xx-coordinate of the vertex of g(x)g(x) is 33 units less than the xx-coordinate of the vertex of f(x)f(x), indicating a shift to the left.
  5. Calculate Shift Magnitude: Calculate the magnitude of the shift. The difference in x-coordinates is 6−3=36 - 3 = 3 units.

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