Final answer:
The equation g(x)=-6(x-3)²+5 represents a quadratic function with horizontal translation, vertical reflection, and vertical transformation.
Step-by-step explanation:
The equation g(x)=-6(x-3)²+5 represents a quadratic function. The transformations represented by this equation are:
- Horizontal translation: The function is shifted 3 units to the right. So, the vertex of the parabola is at (3, 5).
- Vertical reflection: The negative sign in front of the quadratic term reflects the graph of the function vertically, making it open downwards.
- Vertical transformation: The constant term (+5) shifts the entire graph 5 units up from its vertex.