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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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Describe function transformations

Full solution

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

(C) translation

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.

More problems from Describe function transformations

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\newline

\newline

\text{}(A)g(x) = 9|x+2| - 4\text{]}

\newline

\text{}(B)g(x) = 9|x-2| - 4\text{]}

\newline

\text{}(C)g(x)=-9|x-2| +4\text{]}

\newline

\text{(D)}g(x) = -9|x + 2| + 4\text{]}

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\newline

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