Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Let
[tex]$
\begin{array}{l}
f(x) = x^2 \\
g(x) = (x - 3)^2 + 2
\end{array}
$[/tex]

Which transformations are needed to transform the graph of [tex]$f(x)$[/tex] to the graph of [tex]$g(x)$[/tex]? Use the drop-down menus to complete the statements.

Horizontal translation of [tex]$\square$[/tex] Choose... .

Vertical translation of [tex]$\square$[/tex] Choose... .

Sagot :

GinnyAnswer
To transform the graph of [tex]\( f(x) = x^2 \)[/tex] to the graph of [tex]\( g(x) = (x-3)^2 + 2 \)[/tex], we need to apply the following transformations:

1. Horizontal Translation:
- The term [tex]\((x-3)\)[/tex] inside the square function indicates a horizontal translation.
- Since the expression inside the parenthesis is [tex]\( x - 3 \)[/tex], it implies that every point on the graph of [tex]\( f(x) \)[/tex] is shifted to the right by 3 units.

Therefore, the horizontal translation is 3 units to the right.

2. Vertical Translation:
- The constant [tex]\( +2 \)[/tex] outside the square function indicates a vertical translation.
- This means that every point on the graph of [tex]\( f(x) \)[/tex] is shifted upwards by 2 units.

Therefore, the vertical translation is 2 units upwards.

In conclusion:

- Horizontal translation of 3 units to the right.
- Vertical translation of 2 units upwards.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.