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What kind of transformation converts the graph of f(x)=5(x−5)2−6f(x) = 5(x - 5)^2 - 6 into the graph of g(x)=5(x−10)2−6g(x) = 5(x - 10)^2 - 6?\newlineChoices:\newline(A) translation 55 units down\newline(B) translation 55 units up\newline(C) translation 55 units left\newline(D) translation 55 units right

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Q. What kind of transformation converts the graph of f(x)=5(x−5)2−6f(x) = 5(x - 5)^2 - 6 into the graph of g(x)=5(x−10)2−6g(x) = 5(x - 10)^2 - 6?\newlineChoices:\newline(A) translation 55 units down\newline(B) translation 55 units up\newline(C) translation 55 units left\newline(D) translation 55 units right
  1. Compare Functions: To determine the type of transformation, we need to compare the two functions f(x)f(x) and g(x)g(x) and see how the graph of f(x)f(x) has been altered to become the graph of g(x)g(x).
  2. Original and Transformed Functions: The original function is f(x)=5(x−5)2−6f(x) = 5(x - 5)^2 - 6. The transformed function is g(x)=5(x−10)2−6g(x) = 5(x - 10)^2 - 6. We notice that the only change is in the expression inside the parentheses: (x−5)(x - 5) has become (x−10)(x - 10).
  3. Identify Horizontal Shift: The change from (x−5)(x - 5) to (x−10)(x - 10) indicates a horizontal shift. Since the number inside the parentheses has increased from 55 to 1010, this means the graph has been shifted to the right.
  4. Calculate Shift Amount: The amount of the shift is the difference between the two numbers inside the parentheses, which is 10−5=510 - 5 = 5 units. Therefore, the graph has been translated 55 units to the right.

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