What kind of transformation converts the graph of f(x) = 5(x - 2)^2 + 4 into the graph of g(x) = 5(x + 5)^2 + 4? Choices: (A)translation 7 units down (B)translation 7 units up (C)translation 7 units left (D)translation 7 units right

Identify Vertex: Identify the vertex of the function f(x) = 5(x - 2)^2 + 4. The vertex form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. For f(x) = 5(x - 2)^2 + 4, the vertex is at (h, k) = (2, 4).Identify Vertex: Identify the vertex of the function g(x) = 5(x + 5)^2 + 4. Similarly, for g(x) = 5(x + 5)^2 + 4, the vertex is at (h, k) = (-5, 4).Determine Horizontal Shift: Determine the horizontal shift between the vertices of f(x) and g(x). The horizontal shift is the difference in the x-coordinates of the vertices. The x-coordinate of the vertex of f(x) is 2, and the x-coordinate of the vertex of g(x) is -5. The shift is from 2 to -5, which is a shift of 2 - (-5) = 7 units to the left.Determine Vertical Shift: Determine if there is any vertical shift between the vertices of f(x) and g(x). The vertical shift is the difference in the y-coordinates of the vertices. Since both y-coordinates are 4, there is no vertical shift.

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What kind of transformation converts the graph of $f(x) = 5(x - 2)^2 + 4$ into the graph of $g(x) = 5(x + 5)^2 + 4$ ? $\newline$ Choices: $\newline$ (A) translation $7$ units down $\newline$ (B) translation $7$ units up $\newline$ (C) translation $7$ units left $\newline$ (D) translation $7$ units right

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Algebra 2

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 5(x - 2)^2 + 4

into the graph of

g(x) = 5(x + 5)^2 + 4

\newline

Choices:

\newline

(A) translation

7

units down

\newline

(B) translation

7

units up

\newline

7

units left

\newline

(D) translation

7

units right

Identify Vertex: Identify the vertex of the function $f(x) = 5(x - 2)^2 + 4$ . $\newline$ The vertex form of a quadratic function is $f(x) = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. For $f(x) = 5(x - 2)^2 + 4$ , the vertex is at $(h, k) = (2, 4)$ .
Identify Vertex: Identify the vertex of the function $g(x) = 5(x + 5)^2 + 4$ . $\newline$ Similarly, for $g(x) = 5(x + 5)^2 + 4$ , the vertex is at $(h, k) = (-5, 4)$ .
Determine Horizontal Shift: Determine the horizontal shift between the vertices of $f(x)$ and $g(x)$ . The horizontal shift is the difference in the $x$ -coordinates of the vertices. The $x$ -coordinate of the vertex of $f(x)$ is $2$ , and the $x$ -coordinate of the vertex of $g(x)$ is $-5$ . The shift is from $2$ to $-5$ , which is a shift of $g(x)$ $1$ units to the left.
Determine Vertical Shift: Determine if there is any vertical shift between the vertices of $f(x)$ and $g(x)$ . The vertical shift is the difference in the $y$ -coordinates of the vertices. Since both $y$ -coordinates are $4$ , there is no vertical shift.