What kind of transformation converts the graph of f(x) = -6(x + 10)^2 + 2 into the graph of g(x) = -6(x + 4)^2 + 2? Choices: (A)translation 6 units down (B)translation 6 units up (C)translation 6 units right (D)translation 6 units left

Find Vertex: f(x) = -6(x + 10)^2 + 2 Find the vertex of the given function. Compare f(x) = -6(x + 10)^2 + 2 with the vertex form. Vertex of f(x): (-10, 2)Compare Functions: g(x) = -6(x + 4)^2 + 2 Find the vertex of the transformed function. Compare g(x) = -6(x + 4)^2 + 2 with the vertex form. Vertex of g(x): (-4, 2)Find Transformed Vertex: We found: Vertex of f(x) = (-10, 2) Vertex of g(x) = (-4, 2) Is the transformation horizontal or vertical? Since the y-values of the vertices are the same and the x-values change, the transformation is horizontal.Identify Transformation: We have: Vertex of f(x) = (-10, 2) Vertex of g(x) = (-4, 2) Did f(x) shift to the left or right to become g(x)? The x-coordinates of the vertices are -10 and -4 respectively. On a number line, -4 lies to the right of -10. f(x) shifts towards the right.Shift Direction: We found that f(x) shifts towards the right. Identify the transformation from (-10, 2) to (-4, 2). |-10 - (-4)| =|-10 + 4| =|-6| =6 The graph of f(x) shifts 6 units to the right.

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

into the graph of

g(x) = -6(x + 4)^2 + 2

\newline

Choices:

\newline

(A) translation

6

units down

\newline

(B) translation

6

units up

\newline

6

units right

\newline

(D) translation

6

units left

Find Vertex: $f(x) = -6(x + 10)^2 + 2$ $\newline$ Find the vertex of the given function. $\newline$ Compare $f(x) = -6(x + 10)^2 + 2$ with the vertex form. $\newline$ Vertex of $f(x)$ : $(-10, 2)$
Compare Functions: $g(x) = -6(x + 4)^2 + 2$ $\newline$ Find the vertex of the transformed function. $\newline$ Compare $g(x) = -6(x + 4)^2 + 2$ with the vertex form. $\newline$ Vertex of $g(x)$ : $(-4, 2)$
Find Transformed Vertex: We found: $\newline$ Vertex of $f(x) = (-10, 2)$ $\newline$ Vertex of $g(x) = (-4, 2)$ $\newline$ Is the transformation horizontal or vertical? $\newline$ Since the $y$ -values of the vertices are the same and the $x$ -values change, the transformation is horizontal.
Identify Transformation: We have: $\newline$ Vertex of $f(x) = (-10, 2)$ $\newline$ Vertex of $g(x) = (-4, 2)$ $\newline$ Did $f(x)$ shift to the left or right to become $g(x)$ ? $\newline$ The $x$ -coordinates of the vertices are $-10$ and $-4$ respectively. $\newline$ On a number line, $-4$ lies to the right of $-10$ . $\newline$ $f(x)$ shifts towards the right.
Shift Direction: We found that $f(x)$ shifts towards the right. $\newline$ Identify the transformation from $(-10, 2)$ to $(-4, 2)$ . $\newline$ $|-10 - (-4)|$ $\newline$ $=|-10 + 4|$ $\newline$ $=|-6|$ $\newline$ $=6$ $\newline$ The graph of $f(x)$ shifts $6$ units to the right.