What kind of transformation converts the graph of f(x) = -6(x + 9)^2 - 5 into the graph of g(x) = -6(x + 4)^2 - 5? Choices: (A)translation 5 units right (B)translation 5 units down (C)translation 5 units left (D)translation 5 units up

Identify Vertex f(x): Identify the vertex of the function f(x). The function f(x) = -6(x + 9)^2 - 5 is in vertex form, where the vertex is at (-h, k). For f(x), the vertex is at (-9, -5).Identify Vertex g(x): Identify the vertex of the function g(x). The function g(x) = -6(x + 4)^2 - 5 is also in vertex form. For g(x), the vertex is at (-4, -5).Type of Transformation: Determine the type of transformation. The y-coordinates of the vertices of f(x) and g(x) are the same, which means there is no vertical shift. The x-coordinates have changed, indicating a horizontal shift.Direction of Shift: Determine the direction of the horizontal shift. The x-coordinate of the vertex of f(x) is -9, and the x-coordinate of the vertex of g(x) is -4. Since -4 is to the right of -9 on the number line, the graph has shifted to the right.Magnitude of Shift: Calculate the magnitude of the horizontal shift. The difference in the x-coordinates of the vertices is |-9 - (-4)| = |-9 + 4| = |5| = 5. Therefore, the graph of f(x) has shifted 5 units to the right to become the graph of g(x).

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What kind of transformation converts the graph of $f(x) = -6(x + 9)^2 - 5$ into the graph of $g(x) = -6(x + 4)^2 - 5$ ? $\newline$ Choices: $\newline$ (A) translation $5$ units right $\newline$ (B) translation $5$ units down $\newline$ (C) translation $5$ units left $\newline$ (D) translation $5$ units up

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -6(x + 9)^2 - 5

into the graph of

g(x) = -6(x + 4)^2 - 5

\newline

Choices:

\newline

(A) translation

5

units right

\newline

(B) translation

5

units down

\newline

5

units left

\newline

(D) translation

5

units up

Identify Vertex $f(x)$ : Identify the vertex of the function $f(x)$ . The function $f(x) = -6(x + 9)^2 - 5$ is in vertex form, where the vertex is at $(-h, k)$ . For $f(x)$ , the vertex is at $(-9, -5)$ .
Identify Vertex $g(x)$ : Identify the vertex of the function $g(x)$ . The function $g(x) = -6(x + 4)^2 - 5$ is also in vertex form. For $g(x)$ , the vertex is at $(-4, -5)$ .
Type of Transformation: Determine the type of transformation. $\newline$ The $y$ -coordinates of the vertices of $f(x)$ and $g(x)$ are the same, which means there is no vertical shift. The $x$ -coordinates have changed, indicating a horizontal shift.
Direction of Shift: Determine the direction of the horizontal shift. The $x$ -coordinate of the vertex of $f(x)$ is $-9$ , and the $x$ -coordinate of the vertex of $g(x)$ is $-4$ . Since $-4$ is to the right of $-9$ on the number line, the graph has shifted to the right.
Magnitude of Shift: Calculate the magnitude of the horizontal shift. The difference in the x-coordinates of the vertices is $|-9 - (-4)| = |-9 + 4| = |5| = 5$ . Therefore, the graph of $f(x)$ has shifted $5$ units to the right to become the graph of $g(x)$ .