What kind of transformation converts the graph of f(x) = –8(x – 4)^2 + 6 into the graph of g(x) = –8(x + 6)^2 + 6? Choices: [[translation 10 units left][translation 10 units right][translation 10 units up][translation 10 units down]]

Identify vertex of f(x): Identify the vertex of the function f(x). The function f(x) = –8(x – 4)^2 + 6 is in vertex form, where the vertex (h, k) can be found directly from the equation. The vertex of f(x) is at (h, k) = (4, 6).Identify vertex of g(x): Identify the vertex of the function g(x). The function g(x) = –8(x + 6)^2 + 6 is also in vertex form. The vertex of g(x) is at (h, k) = (-6, 6).Determine type of transformation: Determine the type of transformation. The transformation involves a change in the x-coordinate of the vertex while the y-coordinate remains the same. This indicates a horizontal shift.Determine direction of horizontal shift: 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 -6. Since -6 is to the left of 4 on the number line, the graph has shifted to the left.Calculate magnitude of horizontal shift: Calculate the magnitude of the horizontal shift. The shift is the difference between the x-coordinates of the vertices of f(x) and g(x). The shift is |4 - (-6)| = |4 + 6| = |10| = 10 units.

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What kind of transformation converts the graph of $f(x) = -8(x - 4)^2 + 6$ into the graph of $g(x) = -8(x + 6)^2 + 6$ ? $\newline$ Choices: $\newline$ $\text{[A]translation 10 units left}$ $\newline$ $\text{[B]translation 10 units right}$ $\newline$ $\text{[C]translation 10 units up}$ $\newline$ $\text{[D]translation 10 units down}$

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -8(x - 4)^2 + 6

into the graph of

g(x) = -8(x + 6)^2 + 6

\newline

Choices:

\newline

\text{[A]translation 10 units left}

\newline

\text{[B]translation 10 units right}

\newline

\text{[C]translation 10 units up}

\newline

\text{[D]translation 10 units down}

Identify vertex of f(x): Identify the vertex of the function f(x). $\newline$ The function $f(x) = -8(x - 4)^2 + 6$ is in vertex form, where the vertex $(h, k)$ can be found directly from the equation. The vertex of f(x) is at $(h, k) = (4, 6)$ .
Identify vertex of g(x): Identify the vertex of the function g(x). $\newline$ The function g(x) = $-8(x + 6)^2 + 6$ is also in vertex form. The vertex of g(x) is at $(h, k) = (-6, 6)$ .
Determine type of transformation: Determine the type of transformation. $\newline$ The transformation involves a change in the $x$ -coordinate of the vertex while the $y$ -coordinate remains the same. This indicates a horizontal shift.
Determine direction of horizontal shift: 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 $-6$ . Since $-6$ is to the left of $4$ on the number line, the graph has shifted to the left.
Calculate magnitude of horizontal shift: Calculate the magnitude of the horizontal shift. $\newline$ The shift is the difference between the x-coordinates of the vertices of $f(x)$ and $g(x)$ . The shift is $|4 - (-6)| = |4 + 6| = |10| = 10$ units.