1. **State the problem:** We want to identify the shape of the graph of the function $$y = -2x^2 + 15x - 6$$. 2. **Analyze the function form:** This function is a quadratic function because it is of the form $$y = ax^2 + bx + c$$ with $$a = -2$$, $$b = 15$$, and $$c = -6$$. 3. **Recall graph shapes:** Quadratic functions graph as **parabolas**. 4. **Determine the direction:** Since $$a = -2 < 0$$, the parabola opens downward. 5. **Conclusion:** The graph of $$y = -2x^2 + 15x - 6$$ is a **parabola**. **Final answer:** The graph is a parabola described by the quadratic function $$y = -2x^2 + 15x - 6$$.