What kind of transformation converts the graph of f(x) = -2(x + 4)^2 + 3 into the graph of g(x) = -2(x - 4)^2 + 3? Choices: (A)translation 8 units down (B)translation 8 units left (C)translation 8 units up (D)translation 8 units right

Identify Vertex: Identify the vertex of the function f(x). Compare f(x) = -2(x + 4)^2 + 3 with the vertex form of a quadratic function. Vertex of f(x): (-4, 3)Compare Functions: Identify the vertex of the function g(x). Compare g(x) = -2(x - 4)^2 + 3 with the vertex form of a quadratic function. Vertex of g(x): (4, 3)Determine Transformation Type: Determine the type of transformation. The vertex of f(x) is (-4, 3) and the vertex of g(x) is (4, 3). Since the y-values of the vertices are the same and the x-values have changed, the transformation is horizontal.Determine Transformation Direction: Determine the direction of the transformation. The x-coordinate of the vertex of f(x) is -4 and the x-coordinate of the vertex of g(x) is 4. Since the x-coordinate has increased, the graph has shifted to the right.Calculate Transformation Distance: Calculate the distance of the transformation. The difference in x-coordinates of the vertices is 4 - (-4) = 8. The graph of f(x) shifts 8 units to the right.

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What kind of transformation converts the graph of $f(x) = -2(x + 4)^2 + 3$ into the graph of $g(x) = -2(x - 4)^2 + 3$ ? $\newline$ Choices: $\newline$ (A) translation $8$ units down $\newline$ (B) translation $8$ units left $\newline$ (C) translation $8$ units up $\newline$ (D) translation $8$ units right

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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) = -2(x + 4)^2 + 3

into the graph of

g(x) = -2(x - 4)^2 + 3

\newline

Choices:

\newline

(A) translation

8

units down

\newline

(B) translation

8

units left

\newline

8

units up

\newline

(D) translation

8

units right

Identify Vertex: Identify the vertex of the function $f(x)$ . Compare $f(x) = -2(x + 4)^2 + 3$ with the vertex form of a quadratic function. Vertex of $f(x)$ : $(-4, 3)$
Compare Functions: Identify the vertex of the function $g(x)$ . Compare $g(x) = -2(x - 4)^2 + 3$ with the vertex form of a quadratic function. Vertex of $g(x)$ : $(4, 3)$
Determine Transformation Type: Determine the type of transformation. $\newline$ The vertex of $f(x)$ is $(-4, 3)$ and the vertex of $g(x)$ is $(4, 3)$ . $\newline$ Since the $y$ -values of the vertices are the same and the $x$ -values have changed, the transformation is horizontal.
Determine Transformation Direction: Determine the direction of the transformation. The $x$ -coordinate of the vertex of $f(x)$ is $-4$ and the $x$ -coordinate of the vertex of $g(x)$ is $4$ . Since the $x$ -coordinate has increased, the graph has shifted to the right.
Calculate Transformation Distance: Calculate the distance of the transformation. $\newline$ The difference in $x$ -coordinates of the vertices is $4 - (-4) = 8$ . $\newline$ The graph of $f(x)$ shifts $8$ units to the right.