What kind of transformation converts the graph of f(x) = 2(x - 7)^2 - 2 into the graph of g(x) = 2(x - 2)^2 - 2? Choices: (A)translation 5 units down (B)translation 5 units up (C)translation 5 units right (D)translation 5 units left

Identify Vertex f(x): Identify the vertex of the function f(x) = 2(x - 7)^2 - 2. The vertex form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. For f(x), h = 7 and k = -2, so the vertex of f(x) is (7, -2).Identify Vertex g(x): Identify the vertex of the function g(x) = 2(x - 2)^2 - 2. Using the same vertex form, for g(x), h = 2 and k = -2, so the vertex of g(x) is (2, -2).Compare Vertices: Compare the vertices of f(x) and g(x) to determine the type of transformation. The vertex of f(x) is (7, -2) and the vertex of g(x) is (2, -2). The y-coordinates of the vertices are the same, so there is no vertical shift. The x-coordinate of the vertex of g(x) is 5 units less than the x-coordinate of the vertex of f(x), indicating a horizontal shift.Determine Shift Direction: Determine the direction of the horizontal shift. Since the x-coordinate of the vertex of g(x) is less than the x-coordinate of the vertex of f(x), the graph has shifted to the left.Calculate Shift Magnitude: Calculate the magnitude of the horizontal shift. The difference in the x-coordinates of the vertices is 7 - 2 = 5. Therefore, the graph of f(x) has been shifted 5 units to the left to obtain the graph of g(x).

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What kind of transformation converts the graph of $f(x) = 2(x - 7)^2 - 2$ into the graph of $g(x) = 2(x - 2)^2 - 2$ ? $\newline$ Choices: $\newline$ (A) translation $5$ units down $\newline$ (B) translation $5$ units up $\newline$ (C) translation $5$ units right $\newline$ (D) translation $5$ units left

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 2(x - 7)^2 - 2

into the graph of

g(x) = 2(x - 2)^2 - 2

\newline

Choices:

\newline

(A) translation

5

units down

\newline

(B) translation

5

units up

\newline

5

units right

\newline

(D) translation

5

units left

Identify Vertex $f(x)$ : Identify the vertex of the function $f(x) = 2(x - 7)^2 - 2$ . The vertex form of a quadratic function is $f(x) = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. For $f(x)$ , $h = 7$ and $k = -2$ , so the vertex of $f(x)$ is $(7, -2)$ .
Identify Vertex $g(x)$ : Identify the vertex of the function $g(x) = 2(x - 2)^2 - 2$ . Using the same vertex form, for $g(x)$ , $h = 2$ and $k = -2$ , so the vertex of $g(x)$ is $(2, -2)$ .
Compare Vertices: Compare the vertices of $f(x)$ and $g(x)$ to determine the type of transformation. $\newline$ The vertex of $f(x)$ is $(7, -2)$ and the vertex of $g(x)$ is $(2, -2)$ . $\newline$ The $y$ -coordinates of the vertices are the same, so there is no vertical shift. $\newline$ The $x$ -coordinate of the vertex of $g(x)$ is $5$ units less than the $x$ -coordinate of the vertex of $f(x)$ , indicating a horizontal shift.
Determine Shift Direction: Determine the direction of the horizontal shift. Since the $x$ -coordinate of the vertex of $g(x)$ is less than the $x$ -coordinate of the vertex of $f(x)$ , the graph has shifted to the left.
Calculate Shift Magnitude: Calculate the magnitude of the horizontal shift. $\newline$ The difference in the x-coordinates of the vertices is $7 - 2 = 5$ . $\newline$ Therefore, the graph of $f(x)$ has been shifted $5$ units to the left to obtain the graph of $g(x)$ .