What kind of transformation converts the graph of f(x) = 10(x - 4)^2 + 9 into the graph of g(x) = 10(x - 3)^2 + 9? Choices: (A)translation 1 unit down (B)translation 1 unit up (C)translation 1 unit right (D)translation 1 unit left

Identify vertex function: Identify the vertex of the function f(x). Compare f(x) = 10(x - 4)^2 + 9 with the vertex form of a parabola, y = a(x - h)^2 + k, where (h, k) is the vertex. Vertex of f(x): (4, 9)Compare with vertex form: Identify the vertex of the function g(x). Compare g(x) = 10(x - 3)^2 + 9 with the vertex form of a parabola, y = a(x - h)^2 + k. Vertex of g(x): (3, 9)Identify vertex function: Determine the type of transformation. The y-coordinates of the vertices of f(x) and g(x) are the same, so there is no vertical shift. The x-coordinate of the vertex of g(x) is 1 unit less than the x-coordinate of the vertex of f(x), indicating a horizontal shift.Compare with vertex form: Determine the direction of the horizontal shift. The x-coordinate of the vertex of f(x) is 4, and the x-coordinate of the vertex of g(x) is 3. Since 3 is to the left of 4 on the number line, the graph has shifted 1 unit to the left.

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What kind of transformation converts the graph of $f(x) = 10(x - 4)^2 + 9$ into the graph of $g(x) = 10(x - 3)^2 + 9$ ? $\newline$ Choices: $\newline$ (A) translation $1$ unit down $\newline$ (B) translation $1$ unit up $\newline$ (C) translation $1$ unit right $\newline$ (D) translation $1$ unit 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) = 10(x - 4)^2 + 9

into the graph of

g(x) = 10(x - 3)^2 + 9

\newline

Choices:

\newline

(A) translation

1

unit down

\newline

(B) translation

1

unit up

\newline

1

unit right

\newline

(D) translation

1

unit left

Identify vertex function: Identify the vertex of the function $f(x)$ . Compare $f(x) = 10(x - 4)^2 + 9$ with the vertex form of a parabola, $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex. Vertex of $f(x)$ : $(4, 9)$
Compare with vertex form: Identify the vertex of the function $g(x)$ . Compare $g(x) = 10(x - 3)^2 + 9$ with the vertex form of a parabola, $y = a(x - h)^2 + k$ . Vertex of $g(x)$ : $(3, 9)$
Identify vertex function: Determine the type of transformation. $\newline$ The $y$ -coordinates of the vertices of $f(x)$ and $g(x)$ are the same, so there is no vertical shift. $\newline$ The $x$ -coordinate of the vertex of $g(x)$ is $1$ unit less than the $x$ -coordinate of the vertex of $f(x)$ , indicating a horizontal shift.
Compare with vertex form: Determine the direction of the horizontal shift. $\newline$ The x-coordinate of the vertex of $f(x)$ is $4$ , and the x-coordinate of the vertex of $g(x)$ is $3$ . $\newline$ Since $3$ is to the left of $4$ on the number line, the graph has shifted $1$ unit to the left.