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

Identify Vertex: Identify the vertex of the function f(x). Compare f(x) = -7(x - 2)^2 - 4 with the vertex form of a parabola. Vertex of f(x): (2, -4)Compare Functions: Identify the vertex of the transformed function g(x). Compare g(x) = -7(x + 5)^2 - 4 with the vertex form of a parabola. Vertex of g(x): (-5, -4)Determine Transformation Type: Determine the type of transformation. The y-coordinates of the vertices of f(x) and g(x) are the same, so there is no vertical shift. The x-coordinates of the vertices are 2 and -5 respectively, indicating a horizontal shift.Determine Shift Direction: Determine the direction of the horizontal shift. The x-coordinate of the vertex of f(x) is 2, and the x-coordinate of the vertex of g(x) is -5. Since -5 is to the left of 2 on the number line, f(x) shifts to the left to become g(x).Calculate Shift Magnitude: Calculate the magnitude of the horizontal shift. The difference in x-coordinates of the vertices is |2 - (-5)| = |2 + 5| = 7. The graph of f(x) shifts 7 units to the left.

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

into the graph of

g(x) = -7(x + 5)^2 - 4

\newline

Choices:

\newline

(A) translation

7

units up

\newline

(B) translation

7

units left

\newline

7

units down

\newline

(D) translation

7

units right

Identify Vertex: Identify the vertex of the function $f(x)$ . Compare $f(x) = -7(x - 2)^2 - 4$ with the vertex form of a parabola. Vertex of $f(x)$ : $(2, -4)$
Compare Functions: Identify the vertex of the transformed function $g(x)$ . Compare $g(x) = -7(x + 5)^2 - 4$ with the vertex form of a parabola. Vertex of $g(x)$ : $(-5, -4)$
Determine Transformation Type: Determine the type of transformation. $\newline$ The $y$ -coordinates of the vertices of $f(x)$ and $g(x)$ are the same, so there is no vertical shift. $\newline$ The $x$ -coordinates of the vertices are $2$ and $-5$ respectively, indicating a horizontal shift.
Determine Shift Direction: Determine the direction of the horizontal shift. The $x$ -coordinate of the vertex of $f(x)$ is $2$ , and the $x$ -coordinate of the vertex of $g(x)$ is $-5$ . Since $-5$ is to the left of $2$ on the number line, $f(x)$ shifts to the left to become $g(x)$ .
Calculate Shift Magnitude: Calculate the magnitude of the horizontal shift. $\newline$ The difference in x-coordinates of the vertices is $|2 - (-5)| = |2 + 5| = 7$ . $\newline$ The graph of $f(x)$ shifts $7$ units to the left.