What kind of transformation converts the graph of f(x) = 5(x - 1)^2 - 9 into the graph of g(x) = 5(x - 1)^2? Choices: (A)translation 9 units down (B)translation 9 units up (C)translation 9 units left (D)translation 9 units right

Identify Vertex Form: Identify the vertex form of the given functions. The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. For f(x) = 5(x - 1)^2 - 9, the vertex is at (h, k) = (1, -9). For g(x) = 5(x - 1)^2, the vertex is at (h, k) = (1, 0).Compare Vertices: Compare the vertices of f(x) and g(x). The vertex of f(x) is (1, -9) and the vertex of g(x) is (1, 0). The transformation involves a change in the k-value (the y-coordinate of the vertex) from -9 to 0.Determine Transformation Direction: Determine the direction of the transformation. Since the k-value increased from -9 to 0, the graph has moved up.Calculate Transformation Magnitude: Calculate the magnitude of the transformation. The change in the k-value is from -9 to 0, which is an increase of 9 units. Therefore, the graph has been translated 9 units up.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What kind of transformation converts the graph of $f(x) = 5(x - 1)^2 - 9$ into the graph of $g(x) = 5(x - 1)^2$ ? $\newline$ Choices: $\newline$ (A) translation $9$ units down $\newline$ (B) translation $9$ units up $\newline$ (C) translation $9$ units left $\newline$ (D) translation $9$ units right

View step-by-step help

Home

Math Problems

Algebra 1

Describe function transformations

Full solution

Q. What kind of transformation converts the graph of

f(x) = 5(x - 1)^2 - 9

into the graph of

g(x) = 5(x - 1)^2

\newline

Choices:

\newline

(A) translation

9

units down

\newline

(B) translation

9

units up

\newline

9

units left

\newline

(D) translation

9

units right

Identify Vertex Form: Identify the vertex form of the given functions. $\newline$ The vertex form of a quadratic function is given by $f(x) = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola. $\newline$ For $f(x) = 5(x - 1)^2 - 9$ , the vertex is at $(h, k) = (1, -9)$ . $\newline$ For $g(x) = 5(x - 1)^2$ , the vertex is at $(h, k) = (1, 0)$ .
Compare Vertices: Compare the vertices of $f(x)$ and $g(x)$ . The vertex of $f(x)$ is $(1, -9)$ and the vertex of $g(x)$ is $(1, 0)$ . The transformation involves a change in the $k$ -value (the $y$ -coordinate of the vertex) from $-9$ to $0$ .
Determine Transformation Direction: Determine the direction of the transformation. Since the $k$ -value increased from $-9$ to $0$ , the graph has moved up.
Calculate Transformation Magnitude: Calculate the magnitude of the transformation. The change in the $k$ -value is from $-9$ to $0$ , which is an increase of $9$ units. Therefore, the graph has been translated $9$ units up.