Final answer:
The equation involves a rightward horizontal shift by 3 units, a reflection across the x-axis, and an upward vertical shift by 6 units, which results in the vertex of the parabola being at the point (3, 6) and opening downward.
Step-by-step explanation:
The equation y = -(x-3)²+6 represents a parabola that has undergone a series of transformations. The transformations include:
- Horizontal shift: The term (x-3) indicates that the parabola is shifted 3 units to the right of the origin.
- Reflection: The negative sign in front of the quadratic term indicates a reflection across the x-axis, so the parabola opens downward instead of upward.
- Vertical shift: The +6 at the end of the equation indicates that the parabola is shifted upwards by 6 units.
The vertex of this parabola is at the point (3, 6) due to the horizontal and vertical shifts. Since the parabola is reflected, it means that instead of having a minimum value at the vertex, it has a maximum value of 6. The axis of symmetry is the vertical line x = 3.