What kind of transformation converts the graph of f(x) = 7(x + 3)^2 + 9 into the graph of g(x) = 7(x - 4)^2 + 9? Choices: (A)translation 7 units right (B)translation 7 units left (C)translation 7 units up (D)translation 7 units down

Find Vertex: f(x) = 7(x + 3)^2 + 9 Find the vertex of the given function. Compare f(x) = 7(x + 3)^2 + 9 with the vertex form. Vertex of f(x): (-3, 9)Compare Functions: g(x) = 7(x - 4)^2 + 9 Find the vertex of the transformed function. Compare g(x) = 7(x - 4)^2 + 9 with the vertex form. Vertex of g(x): (4, 9)Horizontal or Vertical?: We found: Vertex of f(x) = (-3, 9) Vertex of g(x) = (4, 9) Is the transformation horizontal or vertical? Since the y-values of the vertices are the same and the x-values change, the transformation is horizontal.Left or Right Shift?: We have: Vertex of f(x) = (-3, 9) Vertex of g(x) = (4, 9) Did f(x) shift to the left or right to become g(x)? The x-coordinates of the vertices are -3 and 4 respectively. On a number line, 4 lies to the right of -3. f(x) shifts towards the right.Identify Transformation: We found that f(x) shifts towards the right. Identify the transformation from (-3, 9) to (4, 9). |-3 - 4| =|-7| =7 The graph of f(x) shifts 7 units to the right.

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What kind of transformation converts the graph of $f(x) = 7(x + 3)^2 + 9$ into the graph of $g(x) = 7(x - 4)^2 + 9$ ? $\newline$ (A) translation $7$ units right $\newline$ (B) translation $7$ units left $\newline$ (C) translation $7$ units up $\newline$ (D) translation $7$ 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) = 7(x + 3)^2 + 9

into the graph of

g(x) = 7(x - 4)^2 + 9

\newline

(A) translation

7

units right

\newline

(B) translation

7

units left

\newline

7

units up

\newline

(D) translation

7

units down

Find Vertex: $f(x) = 7(x + 3)^2 + 9$ $\newline$ Find the vertex of the given function. $\newline$ Compare $f(x) = 7(x + 3)^2 + 9$ with the vertex form. $\newline$ Vertex of $f(x)$ : $(-3, 9)$
Compare Functions: $g(x) = 7(x - 4)^2 + 9$ $\newline$ Find the vertex of the transformed function. $\newline$ Compare $g(x) = 7(x - 4)^2 + 9$ with the vertex form. $\newline$ Vertex of $g(x)$ : $(4, 9)$
Horizontal or Vertical?: We found: $\newline$ Vertex of $f(x) = (-3, 9)$ $\newline$ Vertex of $g(x) = (4, 9)$ $\newline$ Is the transformation horizontal or vertical? $\newline$ Since the $y$ -values of the vertices are the same and the $x$ -values change, the transformation is horizontal.
Left or Right Shift?: We have: $\newline$ Vertex of $f(x) = (-3, 9)$ $\newline$ Vertex of $g(x) = (4, 9)$ $\newline$ Did $f(x)$ shift to the left or right to become $g(x)$ ? $\newline$ The $x$ -coordinates of the vertices are $-3$ and $4$ respectively. $\newline$ On a number line, $4$ lies to the right of $-3$ . $\newline$ $f(x)$ shifts towards the right.
Identify Transformation: We found that $f(x)$ shifts towards the right. $\newline$ Identify the transformation from $(-3, 9)$ to $(4, 9)$ . $\newline$ $|-3 - 4|$ $\newline$ $=|-7|$ $\newline$ $=7$ $\newline$ The graph of $f(x)$ shifts $7$ units to the right.