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What kind of transformation converts the graph of f(x)=10(x−5)2+10f(x) = 10(x - 5)^2 + 10 into the graph of g(x)=10(x−5)2g(x) = 10(x - 5)^2?\newlineChoices:\newline(A) translation 1010 units down\newline(B) translation 1010 units left\newline(C) translation 1010 units right\newline(D) translation 1010 units up

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Q. What kind of transformation converts the graph of f(x)=10(x−5)2+10f(x) = 10(x - 5)^2 + 10 into the graph of g(x)=10(x−5)2g(x) = 10(x - 5)^2?\newlineChoices:\newline(A) translation 1010 units down\newline(B) translation 1010 units left\newline(C) translation 1010 units right\newline(D) translation 1010 units up
  1. Analyze Functions: Analyze the given functions to determine the type of transformation. We have f(x)=10(x−5)2+10f(x) = 10(x - 5)^2 + 10 and g(x)=10(x−5)2g(x) = 10(x - 5)^2. 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. Vertical Shift Direction: Determine the direction of the vertical shift.\newlineSince f(x)f(x) has a +10+10 at the end and g(x)g(x) does not, this means that g(x)g(x) is f(x)f(x) shifted downwards by 1010 units.
  3. Horizontal Shift Check: Confirm that the shift is not horizontal.\newlineThere is no change in the (x−5)2(x - 5)^2 part of the function, which means there is no horizontal shift. The transformation is purely vertical.
  4. Conclusion: Conclude the type of transformation.\newlineThe graph of f(x)f(x) has been shifted down by 1010 units to obtain the graph of g(x)g(x). Therefore, the correct transformation is a translation 1010 units down.

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