What kind of transformation converts the graph of f(x) = 5(x - 1)^2 + 1 into the graph of g(x) = 5(x - 1)^2 - 2? Choices: (A)translation 3 units down (B)translation 3 units right (C)translation 3 units left (D)translation 3 units up

Find Vertex Function: f(x) = 5(x - 1)^2 + 1 Find the vertex of the given function. Compare f(x) = 5(x - 1)^2 + 1 with the vertex form y = a(x - h)^2 + k. Vertex of f(x): (1, 1)Compare with Vertex Form: g(x) = 5(x - 1)^2 - 2 Find the vertex of the transformed function. Compare g(x) = 5(x - 1)^2 - 2 with the vertex form y = a(x - h)^2 + k. Vertex of g(x): (1, -2)Find Transformed Function Vertex: We found: Vertex of f(x) = (1, 1) Vertex of g(x) = (1, -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.Identify Vertical Transformation: We have: Vertex of f(x) = (1, 1) Vertex of g(x) = (1, -2) Did f(x) shift up or down to become g(x)? The y-coordinates of the vertices are 1 and -2 respectively. On a number line, -2 lies below 1. f(x) shifts downwards.Identify Direction of Shift: We found that f(x) shifts downwards. Identify the transformation from (1, 1) to (1, -2). |1 - (-2)| =|3| =3 The graph of f(x) shifts 3 units down.

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What kind of transformation converts the graph of $f(x) = 5(x - 1)^2 + 1$ into the graph of $g(x) = 5(x - 1)^2 - 2$ ? $\newline$ Choices: $\newline$ (A) translation $3$ units down $\newline$ (B) translation $3$ units right $\newline$ (C) translation $3$ units left $\newline$ (D) translation $3$ units up

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

into the graph of

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

\newline

Choices:

\newline

(A) translation

3

units down

\newline

(B) translation

3

units right

\newline

3

units left

\newline

(D) translation

3

units up

Find Vertex Function: $f(x) = 5(x - 1)^2 + 1$ $\newline$ Find the vertex of the given function. $\newline$ Compare $f(x) = 5(x - 1)^2 + 1$ with the vertex form $y = a(x - h)^2 + k$ . $\newline$ Vertex of $f(x)$ : $(1, 1)$
Compare with Vertex Form: $g(x) = 5(x - 1)^2 - 2$ $\newline$ Find the vertex of the transformed function. $\newline$ Compare $g(x) = 5(x - 1)^2 - 2$ with the vertex form $y = a(x - h)^2 + k$ . $\newline$ Vertex of $g(x)$ : $(1, -2)$
Find Transformed Function Vertex: We found: $\newline$ Vertex of $f(x) = (1, 1)$ $\newline$ Vertex of $g(x) = (1, -2)$ $\newline$ 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.
Identify Vertical Transformation: We have: $\newline$ Vertex of $f(x) = (1, 1)$ $\newline$ Vertex of $g(x) = (1, -2)$ $\newline$ Did $f(x)$ shift up or down to become $g(x)$ ? $\newline$ The $y$ -coordinates of the vertices are $1$ and $-2$ respectively. $\newline$ On a number line, $-2$ lies below $1$ . $\newline$ $f(x)$ shifts downwards.
Identify Direction of Shift: We found that $f(x)$ shifts downwards. $\newline$ Identify the transformation from $(1, 1)$ to $(1, -2)$ . $\newline$ $|1 - (-2)|$ $\newline$ $=|3|$ $\newline$ $=3$ $\newline$ The graph of $f(x)$ shifts $3$ units down.