What kind of transformation converts the graph of f(x) = -4(x - 7)^2 + 1 into the graph of g(x) = -4x^2 + 1? Choices: (A)translation 7 units left (B)translation 7 units down (C)translation 7 units right (D)translation 7 units up

Find Vertex: f(x) = -4(x - 7)^2 + 1 Find the vertex of the given function. Compare f(x) = -4(x - 7)^2 + 1 with the vertex form y = a(x - h)^2 + k. Vertex of f(x): (7, 1)Compare Functions: g(x) = -4x^2 + 1 Find the vertex of the transformed function. Compare g(x) = -4x^2 + 1 with the vertex form y = ax^2 + k. Vertex of g(x): (0, 1)Horizontal or Vertical?: We found: Vertex of f(x) = (7, 1) Vertex of g(x) = (0, 1) 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.Left or Right Shift?: We have: Vertex of f(x) = (7, 1) Vertex of g(x) = (0, 1) Did f(x) shift to the left or right to become g(x)? The x-coordinates of the vertices are 7 and 0 respectively. On a number line, 0 lies to the left of 7. f(x) shifts towards the left.Identify Transformation: We found that f(x) shifts towards the left. Identify the transformation from (7, 1) to (0, 1). Calculate the distance between the x-coordinates of the vertices. |7 - 0| =|7| =7 The graph of f(x) shifts 7 units to the left.

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What kind of transformation converts the graph of $f(x) = -4(x - 7)^2 + 1$ into the graph of $g(x) = -4x^2 + 1$ ? $\newline$ Choices: $\newline$ (A) translation $7$ units left $\newline$ (B) translation $7$ units down $\newline$ (C) translation $7$ units right $\newline$ (D) translation $7$ 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) = -4(x - 7)^2 + 1

into the graph of

g(x) = -4x^2 + 1

\newline

Choices:

\newline

(A) translation

7

units left

\newline

(B) translation

7

units down

\newline

7

units right

\newline

(D) translation

7

units up

Find Vertex: $f(x) = -4(x - 7)^2 + 1$ $\newline$ Find the vertex of the given function. $\newline$ Compare $f(x) = -4(x - 7)^2 + 1$ with the vertex form $y = a(x - h)^2 + k$ . $\newline$ Vertex of $f(x)$ : $(7, 1)$
Compare Functions: $g(x) = -4x^2 + 1$ $\newline$ Find the vertex of the transformed function. $\newline$ Compare $g(x) = -4x^2 + 1$ with the vertex form $y = ax^2 + k$ . $\newline$ Vertex of $g(x)$ : $(0, 1)$
Horizontal or Vertical?: We found: $\newline$ Vertex of $f(x) = (7, 1)$ $\newline$ Vertex of $g(x) = (0, 1)$ $\newline$ 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.
Left or Right Shift?: We have: $\newline$ Vertex of $f(x) = (7, 1)$ $\newline$ Vertex of $g(x) = (0, 1)$ $\newline$ Did $f(x)$ shift to the left or right to become $g(x)$ ? $\newline$ The $x$ -coordinates of the vertices are $7$ and $0$ respectively. $\newline$ On a number line, $0$ lies to the left of $7$ . $\newline$ $f(x)$ shifts towards the left.
Identify Transformation: We found that $f(x)$ shifts towards the left. $\newline$ Identify the transformation from $(7, 1)$ to $(0, 1)$ . $\newline$ Calculate the distance between the $x$ -coordinates of the vertices. $\newline$ $|7 - 0|$ $\newline$ $=|7|$ $\newline$ $=7$ $\newline$ The graph of $f(x)$ shifts $7$ units to the left.