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What kind of transformation converts the graph of f(x)=7(x−4)2−7f(x) = 7(x - 4)^2 - 7 into the graph of g(x)=7(x−2)2−7g(x) = 7(x - 2)^2 - 7?\newlineChoices:\newline(A) translation 22 units right\newline(B) translation 22 units down\newline(C) translation 22 units up\newline(D) translation 22 units left

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Q. What kind of transformation converts the graph of f(x)=7(x−4)2−7f(x) = 7(x - 4)^2 - 7 into the graph of g(x)=7(x−2)2−7g(x) = 7(x - 2)^2 - 7?\newlineChoices:\newline(A) translation 22 units right\newline(B) translation 22 units down\newline(C) translation 22 units up\newline(D) translation 22 units left
  1. Identify Vertex: Identify the vertex of the function f(x)f(x). The function f(x)=7(x−4)2−7f(x) = 7(x - 4)^2 - 7 is in vertex form, where the vertex is at (h,k)(h, k). In this case, h=4h = 4 and k=−7k = -7, so the vertex of f(x)f(x) is (4,−7)(4, -7).
  2. Identify Vertex: Identify the vertex of the function g(x)g(x). The function g(x)=7(x−2)2−7g(x) = 7(x - 2)^2 - 7 is also in vertex form. Here, h=2h = 2 and k=−7k = -7, so the vertex of g(x)g(x) is (2,−7)(2, -7).
  3. Determine Transformation: Determine the type of transformation.\newlineThe vertex of f(x)f(x) is (4,−7)(4, -7) and the vertex of g(x)g(x) is (2,−7)(2, -7). The yy-coordinates of the vertices are the same, which means there is no vertical shift. The xx-coordinate of the vertex of g(x)g(x) is 22 units less than the xx-coordinate of the vertex of f(x)f(x), which indicates a horizontal shift.
  4. Direction of Shift: Determine the direction of the horizontal shift. Since the xx-coordinate of the vertex of g(x)g(x) is 22 units less than that of f(x)f(x), the graph has shifted to the left by 22 units.

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