What kind of transformation converts the graph of f(x) = -5(x + 2)^2 into the graph of g(x) = -5(x + 2)^2 + 4? Choices: (A)translation 4 units left (B)translation 4 units up (C)translation 4 units down (D)translation 4 units right

Find Vertex of f(x): Look at the original function f(x) = -5(x + 2)^2. Find the vertex of f(x). Vertex of f(x): (-2, 0) because the vertex form is y = a(x - h)^2 + k, where (h, k) is the vertex.Find Vertex of g(x): Now look at the transformed function g(x) = -5(x + 2)^2 + 4. Find the vertex of g(x). Vertex of g(x): (-2, 4) because adding 4 only affects the y-coordinate of the vertex.Compare Vertices: Compare the vertices of f(x) and g(x). Vertex of f(x): (-2, 0) Vertex of g(x): (-2, 4) The x-coordinates are the same, so there's no horizontal shift. The y-coordinate of g(x) is 4 units higher than f(x), so it's a vertical shift.Determine Vertical Shift: Determine the direction of the vertical shift. Since the y-coordinate increased by 4, the graph moved up.Identify Transformation: Identify the transformation. The graph of f(x) moved 4 units up to become g(x).

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What kind of transformation converts the graph of $f(x) = -5(x + 2)^2$ into the graph of $g(x) = -5(x + 2)^2 + 4$ ? $\newline$ Choices: $\newline$ (A) translation $4$ units left $\newline$ (B) translation $4$ units up $\newline$ (C) translation $4$ units down $\newline$ (D) translation $4$ units right

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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) = -5(x + 2)^2

into the graph of

g(x) = -5(x + 2)^2 + 4

\newline

Choices:

\newline

(A) translation

4

units left

\newline

(B) translation

4

units up

\newline

4

units down

\newline

(D) translation

4

units right

Find Vertex of $f(x)$ : Look at the original function $f(x) = -5(x + 2)^2$ . Find the vertex of $f(x)$ . Vertex of $f(x)$ : $(-2, 0)$ because the vertex form is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex.
Find Vertex of g(x): Now look at the transformed function $g(x) = -5(x + 2)^2 + 4$ . Find the vertex of $g(x)$ . Vertex of $g(x)$ : $(-2, 4)$ because adding $4$ only affects the y-coordinate of the vertex.
Compare Vertices: Compare the vertices of $f(x)$ and $g(x)$ . $\newline$ Vertex of $f(x)$ : $(-2, 0)$ $\newline$ Vertex of $g(x)$ : $(-2, 4)$ $\newline$ The $x$ -coordinates are the same, so there's no horizontal shift. $\newline$ The $y$ -coordinate of $g(x)$ is $4$ units higher than $f(x)$ , so it's a vertical shift.
Determine Vertical Shift: Determine the direction of the vertical shift. Since the $y$ -coordinate increased by $4$ , the graph moved up.
Identify Transformation: Identify the transformation. $\newline$ The graph of $f(x)$ moved $4$ units up to become $g(x)$ .