What kind of transformation converts the graph of f(x) = (x + 3)^2 + 4 into the graph of g(x) = (x + 9)^2 + 4? Choices: (A)translation 6 units left (B)translation 6 units up (C)translation 6 units right (D)translation 6 units down

Identify Vertex: Identify the vertex of the function f(x). The function f(x) = (x + 3)^2 + 4 is already in vertex form, y = (x - h)^2 + k, where (h, k) is the vertex of the parabola. For f(x), the vertex is (-3, 4).Determine Transformation Type: Identify the vertex of the function g(x). The function g(x) = (x + 9)^2 + 4 is also in vertex form. The vertex of g(x) is (-9, 4).Direction & Magnitude: Determine the type of transformation. The y-coordinate of the vertex has not changed; it remains 4 in both functions. This indicates that there is no vertical translation. The x-coordinate of the vertex has changed from -3 to -9, which indicates a horizontal translation.Calculate Translation Distance: Determine the direction and magnitude of the horizontal translation. The x-coordinate of the vertex has moved from -3 to -9. This is a shift to the left on the number line because -9 is to the left of -3.Calculate the distance of the horizontal translation. The distance between -3 and -9 on the number line is |-3 - (-9)| = |-3 + 9| = |6| = 6. Therefore, the graph has been translated 6 units to the left.

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What kind of transformation converts the graph of $f(x) = (x + 3)^2 + 4$ into the graph of $g(x) = (x + 9)^2 + 4$ ? $\newline$ Choices: $\newline$ (A) translation $6$ units left $\newline$ (B) translation $6$ units up $\newline$ (C) translation $6$ units right $\newline$ (D) translation $6$ units down

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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) = (x + 3)^2 + 4

into the graph of

g(x) = (x + 9)^2 + 4

\newline

Choices:

\newline

(A) translation

6

units left

\newline

(B) translation

6

units up

\newline

6

units right

\newline

(D) translation

6

units down

Identify Vertex: Identify the vertex of the function $f(x)$ . The function $f(x) = (x + 3)^2 + 4$ is already in vertex form, $y = (x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. For $f(x)$ , the vertex is $(-3, 4)$ .
Determine Transformation Type: Identify the vertex of the function $g(x)$ . The function $g(x) = (x + 9)^2 + 4$ is also in vertex form. The vertex of $g(x)$ is $(-9, 4)$ .
Direction & Magnitude: Determine the type of transformation. $\newline$ The y-coordinate of the vertex has not changed; it remains $4$ in both functions. This indicates that there is no vertical translation. The x-coordinate of the vertex has changed from $-3$ to $-9$ , which indicates a horizontal translation.
Calculate Translation Distance: Determine the direction and magnitude of the horizontal translation. $\newline$ The $x$ -coordinate of the vertex has moved from $-3$ to $-9$ . This is a shift to the left on the number line because $-9$ is to the left of $-3$ .
Calculate Translation Distance: Determine the direction and magnitude of the horizontal translation. The $x$ -coordinate of the vertex has moved from $-3$ to $-9$ . This is a shift to the left on the number line because $-9$ is to the left of $-3$ .Calculate the distance of the horizontal translation. The distance between $-3$ and $-9$ on the number line is $|-3 - (-9)| = |-3 + 9| = |6| = 6$ . Therefore, the graph has been translated $6$ units to the left.