What kind of transformation converts the graph of f(x) = -7(x + 7)^2 - 6 into the graph of g(x) = -7(x + 3)^2 - 6? Choices: (A)translation 4 units right (B)translation 4 units down (C)translation 4 units up (D)translation 4 units left

Identify Vertex: Identify the vertex of the function f(x). Compare f(x) = -7(x + 7)^2 - 6 with the vertex form of a quadratic function. Vertex of f(x): (-7, -6)Compare Functions: Identify the vertex of the transformed function g(x). Compare g(x) = -7(x + 3)^2 - 6 with the vertex form of a quadratic function. Vertex of g(x): (-3, -6)Identify Transformation Type: Determine the type of transformation. Since the y-coordinates of the vertices of f(x) and g(x) are the same, the transformation is horizontal.Determine Transformation Direction: Determine the direction of the transformation. The x-coordinate of the vertex of f(x) is -7, and the x-coordinate of the vertex of g(x) is -3. Since -3 is to the right of -7 on the number line, f(x) shifts to the right to become g(x).Calculate Transformation Magnitude: Calculate the magnitude of the transformation. |-7 - (-3)| = |-7 + 3| = |-4| = 4 The graph of f(x) shifts 4 units to the right.

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What kind of transformation converts the graph of $f(x) = -7(x + 7)^2 - 6$ into the graph of $g(x) = -7(x + 3)^2 - 6$ ? $\newline$ Choices: $\newline$ (A) translation $4$ units right $\newline$ (B) translation $4$ units down $\newline$ (C) translation $4$ units up $\newline$ (D) translation $4$ units left

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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 + 7)^2 - 6

into the graph of

g(x) = -7(x + 3)^2 - 6

\newline

Choices:

\newline

(A) translation

4

units right

\newline

(B) translation

4

units down

\newline

4

units up

\newline

(D) translation

4

units left

Identify Vertex: Identify the vertex of the function $f(x)$ . Compare $f(x) = -7(x + 7)^2 - 6$ with the vertex form of a quadratic function. Vertex of $f(x)$ : $(-7, -6)$
Compare Functions: Identify the vertex of the transformed function $g(x)$ . Compare $g(x) = -7(x + 3)^2 - 6$ with the vertex form of a quadratic function. Vertex of $g(x)$ : $(-3, -6)$
Identify Transformation Type: Determine the type of transformation. Since the $y$ -coordinates of the vertices of $f(x)$ and $g(x)$ are the same, the transformation is horizontal.
Determine Transformation Direction: Determine the direction of the transformation. The $x$ -coordinate of the vertex of $f(x)$ is $-7$ , and the $x$ -coordinate of the vertex of $g(x)$ is $-3$ . Since $-3$ is to the right of $-7$ on the number line, $f(x)$ shifts to the right to become $g(x)$ .
Calculate Transformation Magnitude: Calculate the magnitude of the transformation. $\newline$ $|-7 - (-3)| = |-7 + 3| = |-4| = 4$ $\newline$ The graph of $f(x)$ shifts $4$ units to the right.