What kind of transformation converts the graph of f(x) = -10(x - 3)^2 + 5 into the graph of g(x) = -10(x - 3)^2 - 3? Choices: (A)translation 8 units down (B)translation 8 units left (C)translation 8 units up (D)translation 8 units right

Find Vertex: f(x) = -10(x - 3)^2 + 5 Find the vertex of the given function. Compare f(x) = -10(x - 3)^2 + 5 with vertex form. Vertex of f(x): (3, 5)Compare with Vertex Form: g(x) = -10(x - 3)^2 - 3 Find the vertex of the transformed function. Compare g(x) = -10(x - 3)^2 - 3 with vertex form. Vertex of g(x): (3, -3)Find Transformed Vertex: We found: Vertex of f(x) = (3, 5) Vertex of g(x) = (3, -3) Is the transformation horizontal or vertical? Since the x-values of the vertices are the same and the y-values have changed, the transformation is vertical.Identify Transformation Type: We have: Vertex of f(x) = (3, 5) Vertex of g(x) = (3, -3) Did f(x) shift up or down to become g(x)? The y-coordinates of the vertices are 5 and -3 respectively. On a number line, -3 lies below 5. f(x) shifts downwards.Determine Direction of Shift: We found that f(x) shifts downwards. Identify the transformation from (3, 5) to (3, -3). |5 - (-3)| =|8| =8 The graph of f(x) shifts 8 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 $f(x) = -10(x - 3)^2 + 5$ into the graph of $g(x) = -10(x - 3)^2 - 3$ ? $\newline$ Choices: $\newline$ (A) translation $8$ units down $\newline$ (B) translation $8$ units left $\newline$ (C) translation $8$ units up $\newline$ (D) translation $8$ 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 - 3)^2 + 5

into the graph of

g(x) = -10(x - 3)^2 - 3

\newline

Choices:

\newline

(A) translation

8

units down

\newline

(B) translation

8

units left

\newline

8

units up

\newline

(D) translation

8

units right

Find Vertex: $f(x) = -10(x - 3)^2 + 5$ $\newline$ Find the vertex of the given function. $\newline$ Compare $f(x) = -10(x - 3)^2 + 5$ with vertex form. $\newline$ Vertex of $f(x)$ : $(3, 5)$
Compare with Vertex Form: $g(x) = -10(x - 3)^2 - 3$ $\newline$ Find the vertex of the transformed function. $\newline$ Compare $g(x) = -10(x - 3)^2 - 3$ with vertex form. $\newline$ Vertex of $g(x)$ : $(3, -3)$
Find Transformed Vertex: We found: $\newline$ Vertex of $f(x) = (3, 5)$ $\newline$ Vertex of $g(x) = (3, -3)$ $\newline$ Is the transformation horizontal or vertical? $\newline$ Since the $x$ -values of the vertices are the same and the $y$ -values have changed, the transformation is vertical.
Identify Transformation Type: We have: $\newline$ Vertex of $f(x) = (3, 5)$ $\newline$ Vertex of $g(x) = (3, -3)$ $\newline$ Did $f(x)$ shift up or down to become $g(x)$ ? $\newline$ The $y$ -coordinates of the vertices are $5$ and $-3$ respectively. $\newline$ On a number line, $-3$ lies below $5$ . $\newline$ $f(x)$ shifts downwards.
Determine Direction of Shift: We found that $f(x)$ shifts downwards. $\newline$ Identify the transformation from $(3, 5)$ to $(3, -3)$ . $\newline$ $|5 - (-3)|$ $\newline$ $=|8|$ $\newline$ $=8$ $\newline$ The graph of $f(x)$ shifts $8$ units down.