What kind of transformation converts the graph of f(x) = 7(x - 4)^2 - 7 into the graph of g(x) = 7(x - 2)^2 - 7? Choices: (A)translation 2 units right (B)translation 2 units down (C)translation 2 units up (D)translation 2 units left

Identify Vertex: Identify the vertex of the function f(x). The function f(x) = 7(x - 4)^2 - 7 is in vertex form, where the vertex is at (h, k). In this case, h = 4 and k = -7, so the vertex of f(x) is (4, -7).Identify Vertex: Identify the vertex of the function g(x). The function g(x) = 7(x - 2)^2 - 7 is also in vertex form. Here, h = 2 and k = -7, so the vertex of g(x) is (2, -7).Determine Transformation: Determine the type of transformation. The vertex of f(x) is (4, -7) and the vertex of g(x) is (2, -7). The y-coordinates of the vertices are the same, which means there is no vertical shift. The x-coordinate of the vertex of g(x) is 2 units less than the x-coordinate of the vertex of f(x), which indicates a horizontal shift.Direction of Shift: Determine the direction of the horizontal shift. Since the x-coordinate of the vertex of g(x) is 2 units less than that of f(x), the graph has shifted to the left by 2 units.

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What kind of transformation converts the graph of $f(x) = 7(x - 4)^2 - 7$ into the graph of $g(x) = 7(x - 2)^2 - 7$ ? $\newline$ Choices: $\newline$ (A) translation $2$ units right $\newline$ (B) translation $2$ units down $\newline$ (C) translation $2$ units up $\newline$ (D) translation $2$ units left

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Math Problems

Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 7(x - 4)^2 - 7

into the graph of

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

\newline

Choices:

\newline

(A) translation

2

units right

\newline

(B) translation

2

units down

\newline

2

units up

\newline

(D) translation

2

units left

Identify Vertex: Identify the vertex of the function $f(x)$ . The function $f(x) = 7(x - 4)^2 - 7$ is in vertex form, where the vertex is at $(h, k)$ . In this case, $h = 4$ and $k = -7$ , so the vertex of $f(x)$ is $(4, -7)$ .
Identify Vertex: Identify the vertex of the function $g(x)$ . The function $g(x) = 7(x - 2)^2 - 7$ is also in vertex form. Here, $h = 2$ and $k = -7$ , so the vertex of $g(x)$ is $(2, -7)$ .
Determine Transformation: Determine the type of transformation. $\newline$ The vertex of $f(x)$ is $(4, -7)$ and the vertex of $g(x)$ is $(2, -7)$ . The $y$ -coordinates of the vertices are the same, which means there is no vertical shift. The $x$ -coordinate of the vertex of $g(x)$ is $2$ units less than the $x$ -coordinate of the vertex of $f(x)$ , which indicates a horizontal shift.
Direction of Shift: Determine the direction of the horizontal shift. Since the $x$ -coordinate of the vertex of $g(x)$ is $2$ units less than that of $f(x)$ , the graph has shifted to the left by $2$ units.