The graphs of f(x) and g(x) are shown below: graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 9, 0. If f(x) = (x + 7)2, which of the following is g(x) based on the translation? g(x) = (x + 9)2 g(x) = (x + 5)2 g(x) = (x − 9)2 g(x) = (x − 5)2

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The graphs of f(x) and g(x) are shown below: graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 9, 0. If f(x) = (x + 7)2, which of the following is g(x) based on the translation? g(x) = (x + 9)2 g(x) = (x + 5)2 g(x) = (x − 9)2 g(x) = (x − 5)2

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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The introduction to this problem essentially summarizes an important property of functions: if f(X) plots a function, then f(X+A) plots the same function shifted to the left A units. Likewise, if f(X) plots a function, then f(X-A) plots the same function shifted to the right A units. You are given that f(X) = (X+7)^2 and that the function given by f(X) = (X+7)^2 has a vertex at (-7,0). If you recall the graph of f(X) = X^2, the function has a vertex at (0,0). Thsi means that when f(X) becomes f(X+7), the graph is shifted to the left 7 units. So logically following, what would the g(X) have to be to shift the graph to the left 9 units?

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