What kind of transformation converts the graph of f(x) = 9(x + 6)^2 + 1 into the graph of g(x) = 9(x + 6)^2 - 8? Choices: (A)translation 9 units right (B)translation 9 units left (C)translation 9 units down (D)translation 9 units up

Identify Vertex f(x): Identify the vertex of the function f(x). The function f(x) = 9(x + 6)^2 + 1 is already in vertex form, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. For f(x), the vertex is at (-6, 1).Identify Vertex g(x): Identify the vertex of the function g(x). The function g(x) = 9(x + 6)^2 - 8 is also in vertex form, and since the (x + 6)^2 part is the same as in f(x), the x-coordinate of the vertex will be the same. For g(x), the vertex is at (-6, -8).Type of Transformation: Determine the type of transformation. Since the x-coordinates of the vertices of f(x) and g(x) are the same, there is no horizontal shift. The y-coordinate of the vertex of g(x) is 9 units lower than the y-coordinate of the vertex of f(x) (1 - (-8) = 9). This indicates a vertical shift.Direction of Shift: Determine the direction of the vertical shift. The y-coordinate of the vertex of g(x) is -8, which is less than the y-coordinate of the vertex of f(x), which is 1. This means the graph has moved downwards.Magnitude of Shift: Calculate the magnitude of the vertical shift. The difference in the y-coordinates of the vertices is 1 - (-8) = 9. This means the graph of f(x) has been shifted 9 units down to get the graph of g(x).

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What kind of transformation converts the graph of $f(x) = 9(x + 6)^2 + 1$ into the graph of $g(x) = 9(x + 6)^2 - 8$ ? $\newline$ Choices: $\newline$ (A) translation $9$ units right $\newline$ (B) translation $9$ units left $\newline$ (C) translation $9$ units down $\newline$ (D) translation $9$ units up

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 9(x + 6)^2 + 1

into the graph of

g(x) = 9(x + 6)^2 - 8

\newline

Choices:

\newline

(A) translation

9

units right

\newline

(B) translation

9

units left

\newline

9

units down

\newline

(D) translation

9

units up

Identify Vertex $f(x)$ : Identify the vertex of the function $f(x)$ . The function $f(x) = 9(x + 6)^2 + 1$ is already in vertex form, which is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. For $f(x)$ , the vertex is at $(-6, 1)$ .
Identify Vertex $g(x)$ : Identify the vertex of the function $g(x)$ . The function $g(x) = 9(x + 6)^2 - 8$ is also in vertex form, and since the $(x + 6)^2$ part is the same as in $f(x)$ , the $x$ -coordinate of the vertex will be the same. For $g(x)$ , the vertex is at $(-6, -8)$ .
Type of Transformation: Determine the type of transformation. $\newline$ Since the $x$ -coordinates of the vertices of $f(x)$ and $g(x)$ are the same, there is no horizontal shift. The $y$ -coordinate of the vertex of $g(x)$ is $9$ units lower than the $y$ -coordinate of the vertex of $f(x)$ ( $1 - (-8) = 9$ ). This indicates a vertical shift.
Direction of Shift: Determine the direction of the vertical shift. $\newline$ The y-coordinate of the vertex of $g(x)$ is $-8$ , which is less than the y-coordinate of the vertex of $f(x)$ , which is $1$ . This means the graph has moved downwards.
Magnitude of Shift: Calculate the magnitude of the vertical shift. $\newline$ The difference in the y-coordinates of the vertices is $1 - (-8) = 9$ . This means the graph of $f(x)$ has been shifted $9$ units down to get the graph of $g(x)$ .