What kind of transformation converts the graph of f(x) = -7(x - 10)^2 + 1 into the graph of g(x) = -7(x - 10)^2 - 8? Choices: (A)translation 9 units left (B)translation 9 units down (C)translation 9 units right (D)translation 9 units up

Find Vertex: f(x) = -7(x - 10)^2 + 1 Find the vertex of the given function. Compare f(x) = -7(x - 10)^2 + 1 with the vertex form. Vertex of f(x): (10, 1)Compare with Vertex Form: g(x) = -7(x - 10)^2 - 8 Find the vertex of the transformed function. Compare g(x) = -7(x - 10)^2 - 8 with the vertex form. Vertex of g(x): (10, -8)Vertical Transformation: We found: Vertex of f(x) = (10, 1) Vertex of g(x) = (10, -8) Is the transformation horizontal or vertical? Since the x-values are the same and the y-values changed, the transformation is vertical.Shift Direction: We have: Vertex of f(x) = (10, 1) Vertex of g(x) = (10, -8) Did f(x) shift up or down to become g(x)? The y-coordinates of the vertices are 1 and -8 respectively. On a number line, -8 lies below 1. f(x) shifts downwards.Identify Shift Amount: We found that f(x) shifts downwards. Identify the transformation from (10, 1) to (10, -8). |1 - (-8)| =|1 + 8| =|9| =9 The graph of f(x) shifts 9 units down.

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What kind of transformation converts the graph of $f(x) = -7(x - 10)^2 + 1$ into the graph of $g(x) = -7(x - 10)^2 - 8$ ? $\newline$ Choices: $\newline$ (A) translation $9$ units left $\newline$ (B) translation $9$ units down $\newline$ (C) translation $9$ units right $\newline$ (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) = -7(x - 10)^2 + 1

into the graph of

g(x) = -7(x - 10)^2 - 8

\newline

Choices:

\newline

(A) translation

9

units left

\newline

(B) translation

9

units down

\newline

9

units right

\newline

(D) translation

9

units up

Find Vertex: $f(x) = -7(x - 10)^2 + 1$ $\newline$ Find the vertex of the given function. $\newline$ Compare $f(x) = -7(x - 10)^2 + 1$ with the vertex form. $\newline$ Vertex of $f(x)$ : $(10, 1)$
Compare with Vertex Form: $g(x) = -7(x - 10)^2 - 8$ $\newline$ Find the vertex of the transformed function. $\newline$ Compare $g(x) = -7(x - 10)^2 - 8$ with the vertex form. $\newline$ Vertex of $g(x)$ : $(10, -8)$
Vertical Transformation: We found: $\newline$ Vertex of $f(x) = (10, 1)$ $\newline$ Vertex of $g(x) = (10, -8)$ $\newline$ Is the transformation horizontal or vertical? $\newline$ Since the $x$ -values are the same and the $y$ -values changed, the transformation is vertical.
Shift Direction: We have: $\newline$ Vertex of $f(x) = (10, 1)$ $\newline$ Vertex of $g(x) = (10, -8)$ $\newline$ Did $f(x)$ shift up or down to become $g(x)$ ? $\newline$ The $y$ -coordinates of the vertices are $1$ and $-8$ respectively. $\newline$ On a number line, $-8$ lies below $1$ . $\newline$ $f(x)$ shifts downwards.
Identify Shift Amount: We found that $f(x)$ shifts downwards. $\newline$ Identify the transformation from $(10, 1)$ to $(10, -8)$ . $\newline$ $|1 - (-8)|$ $\newline$ $=|1 + 8|$ $\newline$ $=|9|$ $\newline$ $=9$ $\newline$ The graph of $f(x)$ shifts $9$ units down.