What kind of transformation converts the graph of f(x) = 8(x - 1)^2 + 1 into the graph of g(x) = 8(x - 1)^2 - 2? Choices: (A)translation 3 units down (B)translation 3 units up (C)translation 3 units right (D)translation 3 units left

Identify Vertex Function: Identify the vertex of the function f(x). The function f(x) = 8(x - 1)^2 + 1 is in vertex form, where the vertex is at (h, k) = (1, 1).Identify Vertex Function: Identify the vertex of the function g(x). The function g(x) = 8(x - 1)^2 - 2 is also in vertex form, and since the (x - 1)^2 part is unchanged, the x-coordinate of the vertex remains the same. The y-coordinate of the vertex is now -2. Therefore, the vertex of g(x) is (1, -2).Determine Transformation Type: Determine the type of transformation. Comparing the vertices of f(x) and g(x), we see that the x-coordinate has not changed, so there is no horizontal shift. The y-coordinate has changed from 1 to -2, which indicates a vertical shift.Determine Vertical Shift: Determine the direction and magnitude of the vertical shift. The y-coordinate of the vertex of f(x) is 1, and the y-coordinate of the vertex of g(x) is -2. To go from 1 to -2, we subtract 3. This means the graph has been shifted 3 units down.Match Transformation Choices: Match the transformation to the given choices. The graph of f(x) has been shifted 3 units down to get the graph of g(x). This corresponds to choice (A) translation 3 units down.

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What kind of transformation converts the graph of $f(x) = 8(x - 1)^2 + 1$ into the graph of $g(x) = 8(x - 1)^2 - 2$ ? $\newline$ Choices: $\newline$ (A) translation $3$ units down $\newline$ (B) translation $3$ units up $\newline$ (C) translation $3$ units right $\newline$ (D) translation $3$ 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) = 8(x - 1)^2 + 1

into the graph of

g(x) = 8(x - 1)^2 - 2

\newline

Choices:

\newline

(A) translation

3

units down

\newline

(B) translation

3

units up

\newline

3

units right

\newline

(D) translation

3

units left

Identify Vertex Function: Identify the vertex of the function $f(x)$ . The function $f(x) = 8(x - 1)^2 + 1$ is in vertex form, where the vertex is at $(h, k) = (1, 1)$ .
Identify Vertex Function: Identify the vertex of the function $g(x)$ . The function $g(x) = 8(x - 1)^2 - 2$ is also in vertex form, and since the $(x - 1)^2$ part is unchanged, the $x$ -coordinate of the vertex remains the same. The $y$ -coordinate of the vertex is now $-2$ . Therefore, the vertex of $g(x)$ is $(1, -2)$ .
Determine Transformation Type: Determine the type of transformation. $\newline$ Comparing the vertices of $f(x)$ and $g(x)$ , we see that the $x$ -coordinate has not changed, so there is no horizontal shift. The $y$ -coordinate has changed from $1$ to $-2$ , which indicates a vertical shift.
Determine Vertical Shift: Determine the direction and magnitude of the vertical shift. The $y$ -coordinate of the vertex of $f(x)$ is $1$ , and the $y$ -coordinate of the vertex of $g(x)$ is $-2$ . To go from $1$ to $-2$ , we subtract $3$ . This means the graph has been shifted $3$ units down.
Match Transformation Choices: Match the transformation to the given choices. $\newline$ The graph of $f(x)$ has been shifted $3$ units down to get the graph of $g(x)$ . This corresponds to choice (A) translation $3$ units down.