Answered

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... .



Answer :

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.

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