What kind of transformation converts the graph of f(x) = 10(x - 5)^2 + 4 into the graph of g(x) = 10(x - 5)^2 - 6? Choices: (A)translation 10 units left (B)translation 10 units up (C)translation 10 units down (D)translation 10 units right

Identify Vertex: Identify the vertex of the function f(x). The function f(x) = 10(x - 5)^2 + 4 is in vertex form, where the vertex is at (h, k). Here, h = 5 and k = 4, so the vertex of f(x) is (5, 4).Compare Vertices: Identify the vertex of the function g(x). The function g(x) = 10(x - 5)^2 - 6 is also in vertex form, with the same h = 5 but a different k = -6. Therefore, the vertex of g(x) is (5, -6).Determine Shift: Compare the vertices of f(x) and g(x) to determine the type of transformation. The vertex of f(x) is (5, 4) and the vertex of g(x) is (5, -6). The x-coordinates of the vertices are the same, which means there is no horizontal shift. The y-coordinate of the vertex of g(x) is lower than that of f(x), indicating a vertical shift.Determine the direction and magnitude of the vertical shift. The y-coordinate of the vertex of f(x) is 4, and the y-coordinate of the vertex of g(x) is -6. To go from 4 to -6, we subtract 10: 4 - 10 = -6. This means the graph has been shifted 10 units down.

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 $f(x) = 10(x - 5)^2 + 4$ into the graph of $g(x) = 10(x - 5)^2 - 6$ ? $\newline$ Choices: $\newline$ (A) translation $10$ units left $\newline$ (B) translation $10$ units up $\newline$ (C) translation $10$ units down $\newline$ (D) translation $10$ 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) = 10(x - 5)^2 + 4

into the graph of

g(x) = 10(x - 5)^2 - 6

\newline

Choices:

\newline

(A) translation

10

units left

\newline

(B) translation

10

units up

\newline

10

units down

\newline

(D) translation

10

units right

Identify Vertex: Identify the vertex of the function $f(x)$ . The function $f(x) = 10(x - 5)^2 + 4$ is in vertex form, where the vertex is at $(h, k)$ . Here, $h = 5$ and $k = 4$ , so the vertex of $f(x)$ is $(5, 4)$ .
Compare Vertices: Identify the vertex of the function $g(x)$ . The function $g(x) = 10(x - 5)^2 - 6$ is also in vertex form, with the same $h = 5$ but a different $k = -6$ . Therefore, the vertex of $g(x)$ is $(5, -6)$ .
Determine Shift: Compare the vertices of $f(x)$ and $g(x)$ to determine the type of transformation. $\newline$ The vertex of $f(x)$ is $(5, 4)$ and the vertex of $g(x)$ is $(5, -6)$ . The $x$ -coordinates of the vertices are the same, which means there is no horizontal shift. The $y$ -coordinate of the vertex of $g(x)$ is lower than that of $f(x)$ , indicating a vertical shift.
Determine Shift: Compare the vertices of $f(x)$ and $g(x)$ to determine the type of transformation. $\newline$ The vertex of $f(x)$ is $(5, 4)$ and the vertex of $g(x)$ is $(5, -6)$ . The $x$ -coordinates of the vertices are the same, which means there is no horizontal shift. The $y$ -coordinate of the vertex of $g(x)$ is lower than that of $f(x)$ , indicating a vertical shift.Determine the direction and magnitude of the vertical shift. $\newline$ The $y$ -coordinate of the vertex of $f(x)$ is $g(x)$ $2$ , and the $y$ -coordinate of the vertex of $g(x)$ is $g(x)$ $5$ . To go from $g(x)$ $2$ to $g(x)$ $5$ , we subtract $g(x)$ $8$ : $g(x)$ $9$ . This means the graph has been shifted $g(x)$ $8$ units down.