What kind of transformation converts the graph of f(x) = 6(x + 2)^2 + 2 into the graph of g(x) = 6(x + 3)^2 + 2? Choices: (A)translation 1 unit left (B)translation 1 unit right (C)translation 1 unit down (D)translation 1 unit up

Identify Vertex: Identify the vertex of the function f(x). The function f(x) = 6(x + 2)^2 + 2 is in vertex form, where the vertex is at (-2, 2).Identify Function: Identify the vertex of the function g(x). The function g(x) = 6(x + 3)^2 + 2 is also in vertex form, where the vertex is at (-3, 2).Determine Transformation Type: 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-coordinate of the vertex of g(x) is 1 unit less than the x-coordinate of the vertex of f(x), which indicates a horizontal shift.Determine Shift Direction: Determine the direction of the horizontal shift. The x-coordinate of the vertex of g(x) is -3, which is 1 unit to the left of the x-coordinate of the vertex of f(x), which is -2. Therefore, the graph of f(x) is shifted 1 unit to the left to obtain the graph of g(x).

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What kind of transformation converts the graph of $f(x) = 6(x + 2)^2 + 2$ into the graph of $g(x) = 6(x + 3)^2 + 2$ ? $\newline$ Choices: $\newline$ (A) translation $1$ unit left $\newline$ (B) translation $1$ unit right $\newline$ (C) translation $1$ unit down $\newline$ (D) translation $1$ unit up

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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) = 6(x + 2)^2 + 2

into the graph of

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

\newline

Choices:

\newline

(A) translation

1

unit left

\newline

(B) translation

1

unit right

\newline

1

unit down

\newline

(D) translation

1

unit up

Identify Vertex: Identify the vertex of the function $f(x)$ . The function $f(x) = 6(x + 2)^2 + 2$ is in vertex form, where the vertex is at $(-2, 2)$ .
Identify Function: Identify the vertex of the function $g(x)$ . The function $g(x) = 6(x + 3)^2 + 2$ is also in vertex form, where the vertex is at $(-3, 2)$ .
Determine Transformation Type: 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 $x$ -coordinate of the vertex of $g(x)$ is $1$ unit less than the $x$ -coordinate of the vertex of $f(x)$ , which indicates a horizontal shift.
Determine Shift Direction: Determine the direction of the horizontal shift. The $x$ -coordinate of the vertex of $g(x)$ is $-3$ , which is $1$ unit to the left of the $x$ -coordinate of the vertex of $f(x)$ , which is $-2$ . Therefore, the graph of $f(x)$ is shifted $1$ unit to the left to obtain the graph of $g(x)$ .