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What kind of transformation converts the graph of f(x)=5(x−1)2−9f(x) = 5(x - 1)^2 - 9 into the graph of g(x)=5(x−1)2g(x) = 5(x - 1)^2?\newlineChoices:\newline(A) translation 99 units down\newline(B) translation 99 units up\newline(C) translation 99 units left\newline(D) translation 99 units right

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Q. What kind of transformation converts the graph of f(x)=5(x−1)2−9f(x) = 5(x - 1)^2 - 9 into the graph of g(x)=5(x−1)2g(x) = 5(x - 1)^2?\newlineChoices:\newline(A) translation 99 units down\newline(B) translation 99 units up\newline(C) translation 99 units left\newline(D) translation 99 units right
  1. Identify Vertex Form: Identify the vertex form of the given functions.\newlineThe vertex form of a quadratic function is given by f(x)=a(x−h)2+kf(x) = a(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola.\newlineFor f(x)=5(x−1)2−9f(x) = 5(x - 1)^2 - 9, the vertex is at (h,k)=(1,−9)(h, k) = (1, -9).\newlineFor g(x)=5(x−1)2g(x) = 5(x - 1)^2, the vertex is at (h,k)=(1,0)(h, k) = (1, 0).
  2. Compare Vertices: Compare the vertices of f(x)f(x) and g(x)g(x). The vertex of f(x)f(x) is (1,−9)(1, -9) and the vertex of g(x)g(x) is (1,0)(1, 0). The transformation involves a change in the kk-value (the yy-coordinate of the vertex) from −9-9 to 00.
  3. Determine Transformation Direction: Determine the direction of the transformation. Since the kk-value increased from −9-9 to 00, the graph has moved up.
  4. Calculate Transformation Magnitude: Calculate the magnitude of the transformation. The change in the kk-value is from −9-9 to 00, which is an increase of 99 units. Therefore, the graph has been translated 99 units up.

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