What kind of transformation converts the graph of f(x) = 3(x - 7)^2 + 8 into the graph of g(x) = 3(x - 7)^2 - 2? Choices: (A)translation 10 units right (B)translation 10 units up (C)translation 10 units left (D)translation 10 units down

Find Vertex: f(x) = 3(x - 7)^2 + 8 Find the vertex of the given function. Compare f(x) = 3(x - 7)^2 + 8 with the vertex form y = a(x - h)^2 + k. Vertex of f(x): (7, 8)Compare Functions: g(x) = 3(x - 7)^2 - 2 Find the vertex of the transformed function. Compare g(x) = 3(x - 7)^2 - 2 with the vertex form y = a(x - h)^2 + k. Vertex of g(x): (7, -2)Vertical Transformation: We found: Vertex of f(x) = (7, 8) Vertex of g(x) = (7, -2) Is the transformation horizontal or vertical? Since the x-values of the vertices are the same and the y-values have changed, the transformation is vertical.Shift Direction: We have: Vertex of f(x) = (7, 8) Vertex of g(x) = (7, -2) Did f(x) shift up or down to become g(x)? The y-coordinate of the vertex decreased from 8 to -2. f(x) shifts downwards.Identify Transformation: We found that f(x) shifts downwards. Identify the transformation from (7, 8) to (7, -2). Calculate the vertical distance between the two vertices. |8 - (-2)| = |8 + 2| = |10| = 10 The graph of f(x) shifts 10 units down.

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What kind of transformation converts the graph of $f(x) = 3(x - 7)^2 + 8$ into the graph of $g(x) = 3(x - 7)^2 - 2$ ? $\newline$ Choices: $\newline$ (A) translation $10$ units right $\newline$ (B) translation $10$ units up $\newline$ (C) translation $10$ units left $\newline$ (D) translation $10$ units down

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Math Problems

Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 3(x - 7)^2 + 8

into the graph of

g(x) = 3(x - 7)^2 - 2

\newline

Choices:

\newline

(A) translation

10

units right

\newline

(B) translation

10

units up

\newline

10

units left

\newline

(D) translation

10

units down

Find Vertex: $f(x) = 3(x - 7)^2 + 8$ $\newline$ Find the vertex of the given function. $\newline$ Compare $f(x) = 3(x - 7)^2 + 8$ with the vertex form $y = a(x - h)^2 + k$ . $\newline$ Vertex of $f(x)$ : $(7, 8)$
Compare Functions: $g(x) = 3(x - 7)^2 - 2$ $\newline$ Find the vertex of the transformed function. $\newline$ Compare $g(x) = 3(x - 7)^2 - 2$ with the vertex form $y = a(x - h)^2 + k$ . $\newline$ Vertex of $g(x)$ : $(7, -2)$
Vertical Transformation: We found: $\newline$ Vertex of $f(x) = (7, 8)$ $\newline$ Vertex of $g(x) = (7, -2)$ $\newline$ Is the transformation horizontal or vertical? $\newline$ Since the $x$ -values of the vertices are the same and the $y$ -values have changed, the transformation is vertical.
Shift Direction: We have: $\newline$ Vertex of $f(x) = (7, 8)$ $\newline$ Vertex of $g(x) = (7, -2)$ $\newline$ Did $f(x)$ shift up or down to become $g(x)$ ? $\newline$ The $y$ -coordinate of the vertex decreased from $8$ to $-2$ . $\newline$ $f(x)$ shifts downwards.
Identify Transformation: We found that $f(x)$ shifts downwards. $\newline$ Identify the transformation from $(7, 8)$ to $(7, -2)$ . $\newline$ Calculate the vertical distance between the two vertices. $\newline$ $|8 - (-2)| = |8 + 2| = |10| = 10$ $\newline$ The graph of $f(x)$ shifts $10$ units down.