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

Identify Vertex Function: Identify the vertex of the function f(x). The function f(x) = -5(x + 7)^2 - 5 is in vertex form, where the vertex (h, k) can be found directly from the equation. The vertex of f(x) is at (-7, -5).Identify Vertex Function: Identify the vertex of the function g(x). The function g(x) = -5x^2 - 5 is also in vertex form, with the vertex at (0, -5).Determine Transformation Type: Determine the type of transformation. The vertex of f(x) is at (-7, -5) and the vertex of g(x) is at (0, -5). The y-coordinates of the vertices are the same, so there is no vertical shift. The x-coordinate of the vertex of f(x) is -7, and the x-coordinate of the vertex of g(x) is 0. This indicates a horizontal shift.Determine Horizontal Shift: Determine the direction and magnitude of the horizontal shift. To go from an x-coordinate of -7 to an x-coordinate of 0, you would need to shift the graph to the right by 7 units.Match Transformation Choices: Match the transformation to the given choices. The graph of f(x) has been shifted 7 units to the right to obtain the graph of g(x). This matches choice (D) translation 7 units right.

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

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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 + 7)^2 - 5

into the graph of

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

\newline

Choices:

\newline

(A) translation

7

units down

\newline

(B) translation

7

units up

\newline

7

units left

\newline

(D) translation

7

units right

Identify Vertex Function: Identify the vertex of the function $f(x)$ . The function $f(x) = -5(x + 7)^2 - 5$ is in vertex form, where the vertex $(h, k)$ can be found directly from the equation. The vertex of $f(x)$ is at $(-7, -5)$ .
Identify Vertex Function: Identify the vertex of the function $g(x)$ . The function $g(x) = -5x^2 - 5$ is also in vertex form, with the vertex at $(0, -5)$ .
Determine Transformation Type: Determine the type of transformation. The vertex of $f(x)$ is at $(-7, -5)$ and the vertex of $g(x)$ is at $(0, -5)$ . The $y$ -coordinates of the vertices are the same, so there is no vertical shift. The $x$ -coordinate of the vertex of $f(x)$ is $-7$ , and the $x$ -coordinate of the vertex of $g(x)$ is $(-7, -5)$ $0$ . This indicates a horizontal shift.
Determine Horizontal Shift: Determine the direction and magnitude of the horizontal shift. To go from an x-coordinate of $-7$ to an x-coordinate of $0$ , you would need to shift the graph to the right by $7$ units.
Match Transformation Choices: Match the transformation to the given choices. $\newline$ The graph of $f(x)$ has been shifted $7$ units to the right to obtain the graph of $g(x)$ . This matches choice (D) translation $7$ units right.