What kind of transformation converts the graph of f(x) = -9(x - 8)^2 + 3 into the graph of g(x) = -9(x - 8)^2 - 5? Choices: (A)translation 8 units up (B)translation 8 units right (C)translation 8 units left (D)translation 8 units down

Identify Vertex: Identify the vertex of the function f(x). The function f(x) = -9(x - 8)^2 + 3 is in vertex form, where the vertex is given by (h, k). In this case, the vertex of f(x) is (8, 3).Identify Vertex: Identify the vertex of the function g(x). The function g(x) = -9(x - 8)^2 - 5 is also in vertex form, and the vertex is (h, k). Here, the vertex of g(x) is (8, -5).Compare Vertices: Compare the vertices of f(x) and g(x) to determine the transformation. The vertex of f(x) is (8, 3) and the vertex of g(x) is (8, -5). The x-coordinates of the vertices are the same, which means there is no horizontal shift. The y-coordinate of the vertex of g(x) is lower than that of f(x), indicating a vertical shift.Determine Shift: Determine the direction and magnitude of the vertical shift. To find the vertical shift, we calculate the difference in the y-coordinates of the vertices of f(x) and g(x). The difference is 3 - (-5) = 3 + 5 = 8. Since the y-coordinate of g(x) is lower, the graph has shifted downwards.Identify Transformation: Identify the correct transformation from the given choices. The graph of f(x) has shifted 8 units down to become the graph of g(x). This corresponds to choice (D) translation 8 units down.

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What kind of transformation converts the graph of $f(x) = -9(x - 8)^2 + 3$ into the graph of $g(x) = -9(x - 8)^2 - 5$ ? $\newline$ Choices: $\newline$ (A) translation $8$ units up $\newline$ (B) translation $8$ units right $\newline$ (C) translation $8$ units left $\newline$ (D) translation $8$ units down

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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 - 8)^2 + 3

into the graph of

g(x) = -9(x - 8)^2 - 5

\newline

Choices:

\newline

(A) translation

8

units up

\newline

(B) translation

8

units right

\newline

8

units left

\newline

(D) translation

8

units down

Identify Vertex: Identify the vertex of the function $f(x)$ . The function $f(x) = -9(x - 8)^2 + 3$ is in vertex form, where the vertex is given by $(h, k)$ . In this case, the vertex of $f(x)$ is $(8, 3)$ .
Identify Vertex: Identify the vertex of the function $g(x)$ . The function $g(x) = -9(x - 8)^2 - 5$ is also in vertex form, and the vertex is $(h, k)$ . Here, the vertex of $g(x)$ is $(8, -5)$ .
Compare Vertices: Compare the vertices of $f(x)$ and $g(x)$ to determine the transformation. $\newline$ The vertex of $f(x)$ is $(8, 3)$ and the vertex of $g(x)$ is $(8, -5)$ . The $x$ -coordinates of the vertices are the same, which means there is no horizontal shift. The $y$ -coordinate of the vertex of $g(x)$ is lower than that of $f(x)$ , indicating a vertical shift.
Determine Shift: Determine the direction and magnitude of the vertical shift. $\newline$ To find the vertical shift, we calculate the difference in the $y$ -coordinates of the vertices of $f(x)$ and $g(x)$ . $\newline$ The difference is $3 - (-5) = 3 + 5 = 8$ . $\newline$ Since the $y$ -coordinate of $g(x)$ is lower, the graph has shifted downwards.
Identify Transformation: Identify the correct transformation from the given choices. $\newline$ The graph of $f(x)$ has shifted $8$ units down to become the graph of $g(x)$ . This corresponds to choice (D) translation $8$ units down.