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What kind of transformation converts the graph of f(x)=−5(x+10)2f(x) = -5(x + 10)^2 into the graph of g(x)=−5(x+1)2g(x) = -5(x + 1)^2?\newlineChoices:\newline(A) translation 99 units left\newline(B) translation 99 units right\newline(C) translation 99 units up\newline(D) translation 99 units down

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Q. What kind of transformation converts the graph of f(x)=−5(x+10)2f(x) = -5(x + 10)^2 into the graph of g(x)=−5(x+1)2g(x) = -5(x + 1)^2?\newlineChoices:\newline(A) translation 99 units left\newline(B) translation 99 units right\newline(C) translation 99 units up\newline(D) translation 99 units down
  1. Find Vertex of f(x)f(x): Find the vertex of f(x)f(x).f(x)=−5(x+10)2f(x) = -5(x + 10)^2 has a vertex at (−10,0)(-10, 0).
  2. Find Vertex of g(x)g(x): Find the vertex of g(x)g(x).g(x)=−5(x+1)2g(x) = -5(x + 1)^2 has a vertex at (−1,0)(-1, 0).
  3. Compare X-Values: Compare the xx-values of the vertices to determine the direction of the shift. The xx-value of the vertex of f(x)f(x) is −10-10 and the xx-value of the vertex of g(x)g(x) is −1-1.
  4. Calculate Horizontal Shift: Calculate the horizontal shift from the vertex of f(x)f(x) to the vertex of g(x)g(x).−1−(−10)=9-1 - (-10) = 9 The graph shifts 99 units to the right.

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