What kind of transformation converts the graph of f(x) = 6(x + 1)^2 + 10 into the graph of g(x) = 6(x + 9)^2 + 10? Choices: (A)translation 8 units down (B)translation 8 units right (C)translation 8 units left (D)translation 8 units up

Identify Vertex: Identify the vertex of the function f(x). Compare f(x) = 6(x + 1)^2 + 10 with the vertex form of a parabola. Vertex of f(x): (-1, 10)Compare Functions: Identify the vertex of the function g(x). Compare g(x) = 6(x + 9)^2 + 10 with the vertex form of a parabola. Vertex of g(x): (-9, 10)Type of Transformation: Determine the type of transformation. Since the y-values of the vertices are the same and only the x-values have changed, the transformation is horizontal.Direction of Transformation: Determine the direction of the transformation. The x-coordinate of the vertex of f(x) is -1 and the x-coordinate of the vertex of g(x) is -9. Since -9 is to the left of -1 on the number line, the graph has shifted to the left.Calculate Magnitude: Calculate the magnitude of the transformation. The difference in the x-coordinates of the vertices is |-1 - (-9)| = |8| = 8. The graph of f(x) shifts 8 units to the left to become g(x).

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What kind of transformation converts the graph of $f(x) = 6(x + 1)^2 + 10$ into the graph of $g(x) = 6(x + 9)^2 + 10$ ? $\newline$ Choices: $\newline$ (A) translation $8$ units down $\newline$ (B) translation $8$ units right $\newline$ (C) translation $8$ units left $\newline$ (D) translation $8$ units up

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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 + 1)^2 + 10

into the graph of

g(x) = 6(x + 9)^2 + 10

\newline

Choices:

\newline

(A) translation

8

units down

\newline

(B) translation

8

units right

\newline

8

units left

\newline

(D) translation

8

units up

Identify Vertex: Identify the vertex of the function $f(x)$ . Compare $f(x) = 6(x + 1)^2 + 10$ with the vertex form of a parabola. Vertex of $f(x)$ : $(-1, 10)$
Compare Functions: Identify the vertex of the function $g(x)$ . Compare $g(x) = 6(x + 9)^2 + 10$ with the vertex form of a parabola. Vertex of $g(x)$ : $(-9, 10)$
Type of Transformation: Determine the type of transformation. $\newline$ Since the $y$ -values of the vertices are the same and only the $x$ -values have changed, the transformation is horizontal.
Direction of Transformation: Determine the direction of the transformation. $\newline$ The $x$ -coordinate of the vertex of $f(x)$ is $-1$ and the $x$ -coordinate of the vertex of $g(x)$ is $-9$ . $\newline$ Since $-9$ is to the left of $-1$ on the number line, the graph has shifted to the left.
Calculate Magnitude: Calculate the magnitude of the transformation. $\newline$ The difference in the x-coordinates of the vertices is |-1 - (-9)| = |8| = 8＂).$\newlineThe graph of \$f(x)$ shifts $8$ units to the left to become $g(x)$.