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What kind of transformation converts the graph of f(x)=4(x+9)2+4f(x) = 4(x + 9)^2 + 4 into the graph of g(x)=4(x+9)2−4g(x) = 4(x + 9)^2 - 4?\newlineChoices:\newline(A) translation 88 units down\newline(B) translation 88 units left\newline(C) translation 88 units right\newline(D) translation 88 units up

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Q. What kind of transformation converts the graph of f(x)=4(x+9)2+4f(x) = 4(x + 9)^2 + 4 into the graph of g(x)=4(x+9)2−4g(x) = 4(x + 9)^2 - 4?\newlineChoices:\newline(A) translation 88 units down\newline(B) translation 88 units left\newline(C) translation 88 units right\newline(D) translation 88 units up
  1. Identify Transformation Type: Identify the type of transformation by comparing the two functions. f(x)=4(x+9)2+4f(x) = 4(x + 9)^2 + 4 and g(x)=4(x+9)2−4g(x) = 4(x + 9)^2 - 4 differ only in their constant terms. The quadratic terms are identical, which means there is no horizontal shift. The change is in the vertical direction because the constant term has changed.
  2. Determine Vertical Shift Direction: Determine the direction of the vertical shift. The constant term in f(x)f(x) is +4+4, and in g(x)g(x) it is −4-4. Since the constant term in g(x)g(x) is 44 units less than in f(x)f(x), this indicates a vertical shift downward.
  3. Calculate Vertical Shift Magnitude: Calculate the magnitude of the vertical shift. The difference in the constant terms is 4−(−4)=84 - (-4) = 8. This means the graph of f(x)f(x) has been shifted 88 units down to get the graph of g(x)g(x).

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