What kind of transformation converts the graph of f(x) = -7(x - 2)^2 - 4 into the graph of g(x) = -7(x - 2)^2 + 5? Choices: (A)translation 9 units right (B)translation 9 units up (C)translation 9 units left (D)translation 9 units down

Find Vertex: f(x) = -7(x - 2)^2 - 4 Find the vertex of the given function. Compare f(x) = -7(x - 2)^2 - 4 with vertex form. Vertex of f(x): (2, -4)Compare with Vertex Form: g(x) = -7(x - 2)^2 + 5 Find the vertex of the transformed function. Compare g(x) = -7(x - 2)^2 + 5 with vertex form. Vertex of g(x): (2, 5)Find Transformed Vertex: We found: Vertex of f(x) = (2, -4) Vertex of g(x) = (2, 5) 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 Transformation: We have: Vertex of f(x) = (2, -4) Vertex of g(x) = (2, 5) Did f(x) shift up or down to become g(x)? The y-coordinate of the vertex of g(x) is higher than that of f(x). f(x) shifts upwards.Shift Direction: We found that f(x) shifts upwards. Identify the transformation from (-4) to (5). |5 - (-4)| =|9| =9 The graph of f(x) shifts 9 units up.

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What kind of transformation converts the graph of $f(x) = -7(x - 2)^2 - 4$ into the graph of $g(x) = -7(x - 2)^2 + 5$ ? $\newline$ Choices: $\newline$ (A) translation $9$ units right $\newline$ (B) translation $9$ units up $\newline$ (C) translation $9$ units left $\newline$ (D) translation $9$ 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) = -7(x - 2)^2 - 4

into the graph of

g(x) = -7(x - 2)^2 + 5

\newline

Choices:

\newline

(A) translation

9

units right

\newline

(B) translation

9

units up

\newline

9

units left

\newline

(D) translation

9

units down

Find Vertex: $f(x) = -7(x - 2)^2 - 4$ $\newline$ Find the vertex of the given function. $\newline$ Compare $f(x) = -7(x - 2)^2 - 4$ with vertex form. $\newline$ Vertex of $f(x)$ : $(2, -4)$
Compare with Vertex Form: $g(x) = -7(x - 2)^2 + 5$ $\newline$ Find the vertex of the transformed function. $\newline$ Compare $g(x) = -7(x - 2)^2 + 5$ with vertex form. $\newline$ Vertex of $g(x)$ : $(2, 5)$
Find Transformed Vertex: We found: $\newline$ Vertex of $f(x) = (2, -4)$ $\newline$ Vertex of $g(x) = (2, 5)$ $\newline$ 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 Transformation: We have: $\newline$ Vertex of $f(x) = (2, -4)$ $\newline$ Vertex of $g(x) = (2, 5)$ $\newline$ Did $f(x)$ shift up or down to become $g(x)$ ? $\newline$ The $y$ -coordinate of the vertex of $g(x)$ is higher than that of $f(x)$ . $\newline$ $f(x)$ shifts upwards.
Shift Direction: We found that $f(x)$ shifts upwards. $\newline$ Identify the transformation from $(-4)$ to $(5)$ . $\newline$ $|5 - (-4)|$ $\newline$ $=|9|$ $\newline$ $=9$ $\newline$ The graph of $f(x)$ shifts $9$ units up.