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What kind of transformation converts the graph of f(x)=8(x−3)2−8f(x) = 8(x - 3)^2 - 8 into the graph of g(x)=8(x−3)2−3g(x) = 8(x - 3)^2 - 3?\newlineChoices:\newline(A) translation 55 units up\newline(B) translation 55 units down\newline(C) translation 55 units right\newline(D) translation 55 units left

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Q. What kind of transformation converts the graph of f(x)=8(x−3)2−8f(x) = 8(x - 3)^2 - 8 into the graph of g(x)=8(x−3)2−3g(x) = 8(x - 3)^2 - 3?\newlineChoices:\newline(A) translation 55 units up\newline(B) translation 55 units down\newline(C) translation 55 units right\newline(D) translation 55 units left
  1. Compare Vertices: Compare the yy-values of the vertices of f(x)f(x) and g(x)g(x).\newlinef(x)f(x) has a vertex at (3,−8)(3, -8) since it's in the form 8(x−h)2+k8(x - h)^2 + k.\newlineg(x)g(x) has a vertex at (3,−3)(3, -3) for the same reason.
  2. Determine Change: Determine the change in the y-values of the vertices.\newlineThe y-value of the vertex of g(x)g(x) is 55 units higher than the y-value of the vertex of f(x)f(x).\newline−3−(−8)=5-3 - (-8) = 5
  3. Identify Transformation: Identify the transformation based on the change in y-values.\newlineSince the y-value increased by 55, the graph moved up by 55 units.

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