What kind of transformation converts the graph of f(x) = -4(x + 9)^2 into the graph of g(x) = -4(x + 4)^2? Choices: (A)translation 5 units up (B)translation 5 units right (C)translation 5 units down (D)translation 5 units left

Identify Vertex: Identify the vertex of the function f(x) = -4(x + 9)^2. The vertex form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex. For f(x), the vertex is at (-9, 0).Identify Vertex: Identify the vertex of the function g(x) = -4(x + 4)^2. Using the same vertex form, the vertex of g(x) is at (-4, 0).Determine Transformation: Determine the type of transformation. The vertex of f(x) is at (-9, 0) and the vertex of g(x) is at (-4, 0). The y-coordinates are the same, so there is no vertical shift. The x-coordinate has increased from -9 to -4, indicating a horizontal shift.Determine Shift: Determine the direction and magnitude of the horizontal shift. The x-coordinate of the vertex has moved from -9 to -4, which is a shift to the right. To find the magnitude of the shift, calculate the difference between the x-coordinates of the vertices: |-9 - (-4)| = |-9 + 4| = | -5 | = 5. The graph of f(x) shifts 5 units to the right.

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What kind of transformation converts the graph of $f(x) = -4(x + 9)^2$ into the graph of $g(x) = -4(x + 4)^2$ ? $\newline$ Choices: $\newline$ (A) translation $5$ units up $\newline$ (B) translation $5$ units right $\newline$ (C) translation $5$ units down $\newline$ (D) translation $5$ units left

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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 + 9)^2

into the graph of

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

\newline

Choices:

\newline

(A) translation

5

units up

\newline

(B) translation

5

units right

\newline

5

units down

\newline

(D) translation

5

units left

Identify Vertex: Identify the vertex of the function $f(x) = -4(x + 9)^2$ . The vertex form of a quadratic function is $f(x) = a(x - h)^2 + k$ , where $(h, k)$ is the vertex. For $f(x)$ , the vertex is at $(-9, 0)$ .
Identify Vertex: Identify the vertex of the function $g(x) = -4(x + 4)^2$ . Using the same vertex form, the vertex of $g(x)$ is at $(-4, 0)$ .
Determine Transformation: Determine the type of transformation. $\newline$ The vertex of $f(x)$ is at $(-9, 0)$ and the vertex of $g(x)$ is at $(-4, 0)$ . The $y$ -coordinates are the same, so there is no vertical shift. The $x$ -coordinate has increased from $-9$ to $-4$ , indicating a horizontal shift.
Determine Shift: Determine the direction and magnitude of the horizontal shift. The $x$ -coordinate of the vertex has moved from $-9$ to $-4$ , which is a shift to the right. To find the magnitude of the shift, calculate the difference between the $x$ -coordinates of the vertices: $|-9 - (-4)| = |-9 + 4| = | -5 | = 5$ . The graph of $f(x)$ shifts $5$ units to the right.