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.
