What kind of transformation converts the graph of f(x) = 2(x - 8)^2 + 1 into the graph of g(x) = 2(x - 8)^2 + 3? Choices: (A)translation 2 units up (B)translation 2 units down (C)translation 2 units right (D)translation 2 units left

Identify Vertex: Identify the vertex of the function f(x). The function f(x) = 2(x - 8)^2 + 1 is already in vertex form, y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. The vertex of f(x) is (8, 1).Identify Vertex: Identify the vertex of the function g(x). The function g(x) = 2(x - 8)^2 + 3 is also in vertex form, and since the (x - 8)^2 part is unchanged, the x-coordinate of the vertex remains the same. The vertex of g(x) is (8, 3).Determine Transformation: Determine the type of transformation. Comparing the vertices of f(x) and g(x), we see that the x-coordinate has not changed, so there is no horizontal transformation. The y-coordinate has increased from 1 to 3, which indicates a vertical transformation.Calculate Vertical Shift: Calculate the amount of vertical shift. The change in the y-coordinate of the vertex from f(x) to g(x) is from 1 to 3, which is an increase of 3 - 1 = 2 units.Determine Shift Direction: Determine the direction of the vertical shift. Since the y-coordinate increased, the graph has shifted upwards.

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What kind of transformation converts the graph of $f(x) = 2(x - 8)^2 + 1$ into the graph of $g(x) = 2(x - 8)^2 + 3$ ? $\newline$ Choices: $\newline$ (A) translation $2$ units up $\newline$ (B) translation $2$ units down $\newline$ (C) translation $2$ units right $\newline$ (D) translation $2$ units left

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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) = 2(x - 8)^2 + 1

into the graph of

g(x) = 2(x - 8)^2 + 3

\newline

Choices:

\newline

(A) translation

2

units up

\newline

(B) translation

2

units down

\newline

2

units right

\newline

(D) translation

2

units left

Identify Vertex: Identify the vertex of the function $f(x)$ . The function $f(x) = 2(x - 8)^2 + 1$ is already in vertex form, $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. The vertex of $f(x)$ is $(8, 1)$ .
Identify Vertex: Identify the vertex of the function $g(x)$ . The function $g(x) = 2(x - 8)^2 + 3$ is also in vertex form, and since the $(x - 8)^2$ part is unchanged, the $x$ -coordinate of the vertex remains the same. The vertex of $g(x)$ is $(8, 3)$ .
Determine Transformation: Determine the type of transformation. $\newline$ Comparing the vertices of $f(x)$ and $g(x)$ , we see that the $x$ -coordinate has not changed, so there is no horizontal transformation. $\newline$ The $y$ -coordinate has increased from $1$ to $3$ , which indicates a vertical transformation.
Calculate Vertical Shift: Calculate the amount of vertical shift. The change in the $y$ -coordinate of the vertex from $f(x)$ to $g(x)$ is from $1$ to $3$ , which is an increase of $3 - 1 = 2$ units.
Determine Shift Direction: Determine the direction of the vertical shift. Since the $y$ -coordinate increased, the graph has shifted upwards.