What kind of transformation converts the graph of f(x) = -8(x + 9)^2 - 5 into the graph of g(x) = -8(x + 6)^2 - 5? Choices: (A)translation 3 units right (B)translation 3 units left (C)translation 3 units up (D)translation 3 units down

Find Vertex of f(x): Find the vertex of f(x) by comparing f(x) = -8(x + 9)^2 - 5 with the vertex form. Vertex of f(x): (-9, -5)Find Vertex of g(x): Find the vertex of g(x) by comparing g(x) = -8(x + 6)^2 - 5 with the vertex form. Vertex of g(x): (-6, -5)Determine Transformation Type: Determine if the transformation is horizontal or vertical by comparing the vertices of f(x) and g(x). Since the y-values are the same and the x-values change, the transformation is horizontal.Determine Shift Direction: Determine the direction of the shift by comparing the x-coordinates of the vertices of f(x) and g(x). The x-coordinate of f(x) is -9 and the x-coordinate of g(x) is -6. Since -6 is to the right of -9, f(x) shifts to the right.Calculate Shift Distance: Calculate the distance of the horizontal shift from the vertex of f(x) to the vertex of g(x). |-9 - (-6)| = |-9 + 6| = |-3| = 3 The graph of f(x) shifts 3 units to the right.

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What kind of transformation converts the graph of $f(x) = -8(x + 9)^2 - 5$ into the graph of $g(x) = -8(x + 6)^2 - 5$ ? $\newline$ Choices: $\newline$ (A) translation $3$ units right $\newline$ (B) translation $3$ units left $\newline$ (C) translation $3$ units up $\newline$ (D) translation $3$ 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) = -8(x + 9)^2 - 5

into the graph of

g(x) = -8(x + 6)^2 - 5

\newline

Choices:

\newline

(A) translation

3

units right

\newline

(B) translation

3

units left

\newline

3

units up

\newline

(D) translation

3

units down

Find Vertex of $f(x)$ : Find the vertex of $f(x)$ by comparing $f(x) = -8(x + 9)^2 - 5$ with the vertex form. $\newline$ Vertex of $f(x)$ : $(-9, -5)$
Find Vertex of g(x): Find the vertex of $g(x)$ by comparing $g(x) = -8(x + 6)^2 - 5$ with the vertex form. $\newline$ Vertex of $g(x)$ : $(-6, -5)$
Determine Transformation Type: Determine if the transformation is horizontal or vertical by comparing the vertices of $f(x)$ and $g(x)$ . $\newline$ Since the $y$ -values are the same and the $x$ -values change, the transformation is horizontal.
Determine Shift Direction: Determine the direction of the shift by comparing the $x$ -coordinates of the vertices of $f(x)$ and $g(x)$ . The $x$ -coordinate of $f(x)$ is $-9$ and the $x$ -coordinate of $g(x)$ is $-6$ . Since $-6$ is to the right of $-9$ , $f(x)$ shifts to the right.
Calculate Shift Distance: Calculate the distance of the horizontal shift from the vertex of $f(x)$ to the vertex of $g(x)$ . $\newline$ $|-9 - (-6)| = |-9 + 6| = |-3| = 3$ $\newline$ The graph of $f(x)$ shifts $3$ units to the right.