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What kind of transformation converts the graph of f(x)=10(x+3)2−9f(x) = 10(x + 3)^2 - 9 into the graph of g(x)=10(x+3)2−4g(x) = 10(x + 3)^2 - 4?\newlineChoices:\newline(A) translation 55 units up\newline(B) translation 55 units right\newline(C) translation 55 units down\newline(D) translation 55 units left

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Q. What kind of transformation converts the graph of f(x)=10(x+3)2−9f(x) = 10(x + 3)^2 - 9 into the graph of g(x)=10(x+3)2−4g(x) = 10(x + 3)^2 - 4?\newlineChoices:\newline(A) translation 55 units up\newline(B) translation 55 units right\newline(C) translation 55 units down\newline(D) translation 55 units left
  1. Analyze Functions: Analyze the given functions to determine the type of transformation.\newlineWe have f(x)=10(x+3)2−9f(x) = 10(x + 3)^2 - 9 and g(x)=10(x+3)2−4g(x) = 10(x + 3)^2 - 4. The only difference between f(x)f(x) and g(x)g(x) is the constant term at the end of the equation. This indicates a vertical shift.
  2. Determine Shift Direction: Determine the direction of the vertical shift.\newlineSince the constant term in g(x)g(x) is greater than the constant term in f(x)f(x) (−4>−9-4 > -9), the graph of g(x)g(x) is shifted upwards compared to the graph of f(x)f(x).
  3. Calculate Shift Magnitude: Calculate the magnitude of the vertical shift. The difference in the constant terms is −4−(−9)=−4+9=5-4 - (-9) = -4 + 9 = 5. This means the graph of g(x)g(x) is shifted 55 units up from the graph of f(x)f(x).

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