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

Analyze Functions: Analyze the given functions. We have the original function f(x) = -8x^2 - 2 and the transformed function g(x) = -8(x + 8)^2 - 2. We need to determine the type of transformation that occurs between these two functions.Compare Functions: Compare the two functions. The original function f(x) is in the form of -8x^2 - 2, which is a parabola facing downwards with its vertex at the origin (0, -2). The transformed function g(x) is in the form of -8(x + 8)^2 - 2, which is also a parabola facing downwards. The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Identify Vertex: Identify the vertex of the transformed function. The vertex form of g(x) is -8(x - (-8))^2 - 2, which means the vertex of g(x) is at (-8, -2).Determine Transformation Type: Determine the type of transformation. The vertex of f(x) is at (0, -2) and the vertex of g(x) is at (-8, -2). The y-coordinate of the vertex has not changed, so there is no vertical translation. The x-coordinate of the vertex has changed from 0 to -8, which indicates a horizontal translation.Determine Translation Magnitude: Determine the direction and magnitude of the horizontal translation. The x-coordinate of the vertex has moved from 0 to -8, which means the graph has shifted 8 units to the left.

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

into the graph of

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

\newline

Choices:

\newline

(A) translation

8

units left

\newline

(B) translation

8

units up

\newline

8

units down

\newline

(D) translation

8

units right

Analyze Functions: Analyze the given functions. $\newline$ We have the original function $f(x) = -8x^2 - 2$ and the transformed function $g(x) = -8(x + 8)^2 - 2$ . We need to determine the type of transformation that occurs between these two functions.
Compare Functions: Compare the two functions. $\newline$ The original function $f(x)$ is in the form of $-8x^2 - 2$ , which is a parabola facing downwards with its vertex at the origin $(0, -2)$ . The transformed function $g(x)$ is in the form of $-8(x + 8)^2 - 2$ , which is also a parabola facing downwards. The vertex form of a parabola is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Identify Vertex: Identify the vertex of the transformed function. $\newline$ The vertex form of $g(x)$ is $-8(x - (-8))^2 - 2$ , which means the vertex of $g(x)$ is at $(-8, -2)$ .
Determine Transformation Type: Determine the type of transformation. $\newline$ The vertex of $f(x)$ is at $(0, -2)$ and the vertex of $g(x)$ is at $(-8, -2)$ . The $y$ -coordinate of the vertex has not changed, so there is no vertical translation. The $x$ -coordinate of the vertex has changed from $0$ to $-8$ , which indicates a horizontal translation.
Determine Translation Magnitude: Determine the direction and magnitude of the horizontal translation. $\newline$ The $x$ -coordinate of the vertex has moved from $0$ to $-8$ , which means the graph has shifted $8$ units to the left.