Final answer:
The Correct option is B). The function h(x) is transformed from the parent function f(x)=x² by a vertical translation of 3 units up and a horizontal translation of 2 units to the left.
Step-by-step explanation:
For h(x)=(x−2)² +3, the transformations from the parent function f(x)=x² can be determined by analyzing the equation of h(x). The term (x-2)² indicates a horizontal shift: because the x-value is reduced by 2, this is a shift horizontally to the right side of the coordinate system by 2 units. The +3 at the end suggests there is a vertical translation because this term adds a constant to the outcome of the square function, hence the graph moves vertically upward in the coordinate system by 3 units.
Therefore, the correct transformation for h(x) is a vertical translation 3 units up, and a horizontal translation 2 units left, matching option B.