What kind of transformation converts the graph of f(x) = -5(x + 8)^2 + 9 into the graph of g(x) = -5(x + 8)^2 + 1? Choices: (A)translation 8 units left (B)translation 8 units up (C)translation 8 units down (D)translation 8 units right

Identify vertex function: Identify the vertex of the function f(x). The function f(x) = -5(x + 8)^2 + 9 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 (-8, 9).Identify vertex function: Identify the vertex of the function g(x). The function g(x) = -5(x + 8)^2 + 1 is also in vertex form. For g(x), the vertex is (-8, 1).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 transformation. The y-coordinate has changed from 9 to 1, which indicates a vertical transformation.Determine direction magnitude: Determine the direction and magnitude of the vertical transformation. The y-coordinate of the vertex of f(x) is 9, and the y-coordinate of the vertex of g(x) is 1. To go from 9 to 1, we subtract 8, which means the graph has moved 8 units down.Match transformation choices: Match the transformation to the given choices. The graph has moved 8 units down, which corresponds to choice (C) translation 8 units down.

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What kind of transformation converts the graph of $f(x) = -5(x + 8)^2 + 9$ into the graph of $g(x) = -5(x + 8)^2 + 1$ ? $\newline$ Choices: $\newline$ (A) translation $8$ units left $\newline$ (B) translation $8$ units up $\newline$ (C) translation $8$ units down $\newline$ (D) translation $8$ units right

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -5(x + 8)^2 + 9

into the graph of

g(x) = -5(x + 8)^2 + 1

\newline

Choices:

\newline

(A) translation

8

units left

\newline

(B) translation

8

units up

\newline

8

units down

\newline

(D) translation

8

units right

Identify vertex function: Identify the vertex of the function $f(x)$ . The function $f(x) = -5(x + 8)^2 + 9$ 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 $(-8, 9)$ .
Identify vertex function: Identify the vertex of the function $g(x)$ . The function $g(x) = -5(x + 8)^2 + 1$ is also in vertex form. For $g(x)$ , the vertex is $(-8, 1)$ .
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 transformation. $\newline$ The $y$ -coordinate has changed from $9$ to $1$ , which indicates a vertical transformation.
Determine direction magnitude: Determine the direction and magnitude of the vertical transformation. $\newline$ The $y$ -coordinate of the vertex of $f(x)$ is $9$ , and the $y$ -coordinate of the vertex of $g(x)$ is $1$ . $\newline$ To go from $9$ to $1$ , we subtract $8$ , which means the graph has moved $8$ units down.
Match transformation choices: Match the transformation to the given choices. $\newline$ The graph has moved $8$ units down, which corresponds to choice (C) translation $8$ units down.