What kind of transformation converts the graph of f(x) = -5(x - 2)^2 - 10 into the graph of g(x) = -5(x - 4)^2 - 10? Choices: (A)translation 2 units up (B)translation 2 units right (C)translation 2 units left (D)translation 2 units down

Find Vertex Function: f(x) = -5(x - 2)^2 - 10 Find the vertex of the given function. Compare f(x) = -5(x - 2)^2 - 10 with vertex form. Vertex of f(x): (2, -10)Compare with Vertex Form: g(x) = -5(x - 4)^2 - 10 Find the vertex of the transformed function. Compare g(x) = -5(x - 4)^2 - 10 with vertex form. Vertex of g(x): (4, -10)Find Transformed Vertex: We found: Vertex of f(x) = (2, -10) Vertex of g(x) = (4, -10) Is the transformation horizontal or vertical? Since the y-values of the vertices are the same and the x-values have changed, the transformation is horizontal.Compare with Vertex Form: We have: Vertex of f(x) = (2, -10) Vertex of g(x) = (4, -10) Did f(x) shift to the left or right to become g(x)? x-coordinates of the vertices are 2 and 4 respectively. On a number line, 4 lies to the right of 2. f(x) shifts towards right.Identify Transformation: We found that, f(x) shifts towards right. Identify the transformation from (2, -10) to (4, -10). |2 - 4| =|-2| =2 The graph of f(x) shifts 2 units to the right.

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What kind of transformation converts the graph of $f(x) = -5(x - 2)^2 - 10$ into the graph of $g(x) = -5(x - 4)^2 - 10$ ? $\newline$ Choices: $\newline$ (A) translation $2$ units up $\newline$ (B) translation $2$ units right $\newline$ (C) translation $2$ units left $\newline$ (D) translation $2$ 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) = -5(x - 2)^2 - 10

into the graph of

g(x) = -5(x - 4)^2 - 10

\newline

Choices:

\newline

(A) translation

2

units up

\newline

(B) translation

2

units right

\newline

2

units left

\newline

(D) translation

2

units down

Find Vertex Function: $f(x) = -5(x - 2)^2 - 10$ $\newline$ Find the vertex of the given function. $\newline$ Compare $f(x) = -5(x - 2)^2 - 10$ with vertex form. $\newline$ Vertex of $f(x)$ : $(2, -10)$
Compare with Vertex Form: $g(x) = -5(x - 4)^2 - 10$ $\newline$ Find the vertex of the transformed function. $\newline$ Compare $g(x) = -5(x - 4)^2 - 10$ with vertex form. $\newline$ Vertex of $g(x)$ : $(4, -10)$
Find Transformed Vertex: We found: $\newline$ Vertex of $f(x) = (2, -10)$ $\newline$ Vertex of $g(x) = (4, -10)$ $\newline$ Is the transformation horizontal or vertical? $\newline$ Since the $y$ -values of the vertices are the same and the $x$ -values have changed, the transformation is horizontal.
Compare with Vertex Form: We have: $\newline$ Vertex of $f(x)$ = $(2, -10)$ $\newline$ Vertex of $g(x)$ = $(4, -10)$ $\newline$ Did $f(x)$ shift to the left or right to become $g(x)$ ? $\newline$ x-coordinates of the vertices are $2$ and $4$ respectively. $\newline$ On a number line, $4$ lies to the right of $2$ . $\newline$ $f(x)$ shifts towards right.
Identify Transformation: We found that, $f(x)$ shifts towards right. Identify the transformation from $(2, -10)$ to $(4, -10)$ . $|2 - 4| = |-2| = 2$ The graph of $f(x)$ shifts $2$ units to the right.