What kind of transformation converts the graph of f(x) = 4(x - 5)^2 + 10 into the graph of g(x) = 4(x - 5)^2 + 4? Choices: (A)translation 6 units down (B)translation 6 units left (C)translation 6 units up (D)translation 6 units right

Identify Vertex f(x): Identify the vertex of the function f(x) = 4(x - 5)^2 + 10. The function is already in vertex form, f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Here, h = 5 and k = 10. Vertex of f(x): (5, 10)Identify Vertex g(x): Identify the vertex of the function g(x) = 4(x - 5)^2 + 4. The function is also in vertex form, g(x) = a(x - h)^2 + k. Here, h = 5 and k = 4. Vertex of g(x): (5, 4)Determine Vertex Difference: Determine the difference between the vertices of the original and transformed functions. The x-coordinates of the vertices are the same, so there is no horizontal shift. The y-coordinate of the vertex of g(x) is 4, which is 6 units less than the y-coordinate of the vertex of f(x), which is 10. This indicates a vertical shift of 6 units down.

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What kind of transformation converts the graph of $f(x) = 4(x - 5)^2 + 10$ into the graph of $g(x) = 4(x - 5)^2 + 4$ ? $\newline$ Choices: $\newline$ (A) translation $6$ units down $\newline$ (B) translation $6$ units left $\newline$ (C) translation $6$ units up $\newline$ (D) translation $6$ units right

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Math Problems

Algebra 2

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 4(x - 5)^2 + 10

into the graph of

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

\newline

Choices:

\newline

(A) translation

6

units down

\newline

(B) translation

6

units left

\newline

6

units up

\newline

(D) translation

6

units right

Identify Vertex $f(x)$ : Identify the vertex of the function $f(x) = 4(x - 5)^2 + 10$ . The function is already in vertex form, $f(x) = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. Here, $h = 5$ and $k = 10$ . Vertex of $f(x)$ : $(5, 10)$
Identify Vertex $g(x)$ : Identify the vertex of the function $g(x) = 4(x - 5)^2 + 4$ . The function is also in vertex form, $g(x) = a(x - h)^2 + k$ . Here, $h = 5$ and $k = 4$ . Vertex of $g(x)$ : $(5, 4)$
Determine Vertex Difference: Determine the difference between the vertices of the original and transformed functions. $\newline$ The $x$ -coordinates of the vertices are the same, so there is no horizontal shift. $\newline$ The $y$ -coordinate of the vertex of $g(x)$ is $4$ , which is $6$ units less than the $y$ -coordinate of the vertex of $f(x)$ , which is $10$ . $\newline$ This indicates a vertical shift of $6$ units down.