What kind of transformation converts the graph of f(x) = -9(x - 9)^2 - 9 into the graph of g(x) = -9(x + 1)^2 - 9? Choices: (A)translation 10 units left (B)translation 10 units up (C)translation 10 units right (D)translation 10 units down

Find Vertex of f(x): Analyze the given function f(x) = -9(x - 9)^2 - 9 to find its vertex. 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), the vertex is at (h, k) = (9, -9).Find Vertex of g(x): Analyze the transformed function g(x) = -9(x + 1)^2 - 9 to find its vertex. Using the vertex form, the vertex of g(x) is at (h, k) = (-1, -9).Compare Vertices for Transformation: Determine the type of transformation by comparing the vertices of f(x) and g(x). The vertex of f(x) is (9, -9), and the vertex of g(x) is (-1, -9). Since the y-coordinates of the vertices are the same, there is no vertical shift. The x-coordinate of the vertex of g(x) is 10 units to the left of the x-coordinate of the vertex of f(x).Calculate Horizontal Shift: Calculate the exact horizontal shift from the vertex of f(x) to the vertex of g(x). The shift is the difference in the x-coordinates of the vertices: 9 - (-1) = 9 + 1 = 10. The graph of f(x) is shifted 10 units to the left to obtain the graph of g(x).

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What kind of transformation converts the graph of $f(x) = -9(x - 9)^2 - 9$ into the graph of $g(x) = -9(x + 1)^2 - 9$ ? $\newline$ Choices: $\newline$ (A) translation $10$ units left $\newline$ (B) translation $10$ units up $\newline$ (C) translation $10$ units right $\newline$ (D) translation $10$ units down

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -9(x - 9)^2 - 9

into the graph of

g(x) = -9(x + 1)^2 - 9

\newline

Choices:

\newline

(A) translation

10

units left

\newline

(B) translation

10

units up

\newline

10

units right

\newline

(D) translation

10

units down

Find Vertex of $f(x)$ : Analyze the given function $f(x) = -9(x - 9)^2 - 9$ to find its vertex. $\newline$ The vertex form of a quadratic function is $f(x) = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. $\newline$ For $f(x)$ , the vertex is at $(h, k) = (9, -9)$ .
Find Vertex of $g(x)$ : Analyze the transformed function $g(x) = -9(x + 1)^2 - 9$ to find its vertex. $\newline$ Using the vertex form, the vertex of $g(x)$ is at $(h, k) = (-1, -9)$ .
Compare Vertices for Transformation: Determine the type of transformation by comparing the vertices of $f(x)$ and $g(x)$ . The vertex of $f(x)$ is $(9, -9)$ , and the vertex of $g(x)$ is $(-1, -9)$ . Since the $y$ -coordinates of the vertices are the same, there is no vertical shift. The $x$ -coordinate of the vertex of $g(x)$ is $10$ units to the left of the $x$ -coordinate of the vertex of $f(x)$ .
Calculate Horizontal Shift: Calculate the exact horizontal shift from the vertex of $f(x)$ to the vertex of $g(x)$ . The shift is the difference in the $x$ -coordinates of the vertices: $9 - (-1) = 9 + 1 = 10$ . The graph of $f(x)$ is shifted $10$ units to the left to obtain the graph of $g(x)$ .