What kind of transformation converts the graph of f(x) = -4(x - 1)^2 - 1 into the graph of g(x) = -4(x - 1)^2 + 4? Choices: (A)translation 5 units left (B)translation 5 units right (C)translation 5 units down (D)translation 5 units up

Identify Vertex f(x): Identify the vertex of the function f(x). The function f(x) = -4(x - 1)^2 - 1 is already in vertex form, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. For f(x), the vertex is at (h, k) = (1, -1).Identify Vertex g(x): Identify the vertex of the function g(x). The function g(x) = -4(x - 1)^2 + 4 is also in vertex form. For g(x), the vertex is at (h, k) = (1, 4).Compare Vertices Transformation: Compare the vertices of f(x) and g(x) to determine the type of transformation. The vertex of f(x) is (1, -1) and the vertex of g(x) is (1, 4). Since the x-coordinates of the vertices are the same, there is no horizontal transformation. The y-coordinate of the vertex of g(x) is 5 units higher than the y-coordinate of the vertex of f(x). This indicates a vertical transformation.Determine Vertical Transformation: Determine the direction of the vertical transformation. The y-coordinate of the vertex of g(x) is greater than the y-coordinate of the vertex of f(x). This means the graph has moved up.Calculate Vertical Shift: Calculate the exact number of units the graph has moved vertically. The difference in the y-coordinates of the vertices is 4 - (-1) = 5 units. Therefore, the graph of f(x) has been translated 5 units up to become the graph of g(x).

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What kind of transformation converts the graph of $f(x) = -4(x - 1)^2 - 1$ into the graph of $g(x) = -4(x - 1)^2 + 4$ ? $\newline$ Choices: $\newline$ (A) translation $5$ units left $\newline$ (B) translation $5$ units right $\newline$ (C) translation $5$ units down $\newline$ (D) translation $5$ units up

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -4(x - 1)^2 - 1

into the graph of

g(x) = -4(x - 1)^2 + 4

\newline

Choices:

\newline

(A) translation

5

units left

\newline

(B) translation

5

units right

\newline

5

units down

\newline

(D) translation

5

units up

Identify Vertex $f(x)$ : Identify the vertex of the function $f(x)$ . The function $f(x) = -4(x - 1)^2 - 1$ is already in vertex form, which is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. For $f(x)$ , the vertex is at $(h, k) = (1, -1)$ .
Identify Vertex $g(x)$ : Identify the vertex of the function $g(x)$ . The function $g(x) = -4(x - 1)^2 + 4$ is also in vertex form. For $g(x)$ , the vertex is at $(h, k) = (1, 4)$ .
Compare Vertices Transformation: Compare the vertices of $f(x)$ and $g(x)$ to determine the type of transformation. $\newline$ The vertex of $f(x)$ is $(1, -1)$ and the vertex of $g(x)$ is $(1, 4)$ . $\newline$ Since the $x$ -coordinates of the vertices are the same, there is no horizontal transformation. $\newline$ The $y$ -coordinate of the vertex of $g(x)$ is $5$ units higher than the $y$ -coordinate of the vertex of $f(x)$ . $\newline$ This indicates a vertical transformation.
Determine Vertical Transformation: Determine the direction of the vertical transformation. $\newline$ The $y$ -coordinate of the vertex of $g(x)$ is greater than the $y$ -coordinate of the vertex of $f(x)$ . $\newline$ This means the graph has moved up.
Calculate Vertical Shift: Calculate the exact number of units the graph has moved vertically. $\newline$ The difference in the $y$ -coordinates of the vertices is $4 - (-1) = 5$ units. $\newline$ Therefore, the graph of $f(x)$ has been translated $5$ units up to become the graph of $g(x)$ .