1. The problem involves plotting multiple quadratic equations to form a butterfly shape. 2. Each equation represents a part of the butterfly: right wing, left wing, upper and lower body, and decorations. 3. The right wing parabola is given by $$y = -\frac{1}{4}(x - 1)^2 + 3$$, which opens downward and is shifted right by 1 and up by 3. 4. The left wing parabola is $$y = -\frac{1}{4}(x + 1)^2 + 3$$, which is symmetric to the right wing but shifted left by 1. 5. The upper part of the body described by $$y = -\frac{1}{2}x^2 + 4$$ opens downward with a steeper curve and is shifted up by 4. 6. The lower part of the body is $$y = \frac{1}{2}x^2 - 1$$, which opens upward and is shifted down by 1. 7. The decorations on the right and left upper wings use $$y = -\frac{1}{8}(x - 0.5)^2 + 3.5$$ and $$y = -\frac{1}{8}(x + 0.5)^2 + 3.5$$ respectively. 8. The right and left lower decorations are given by $$y = -\frac{1}{8}(x - 0.5)^2 + 2$$ and $$y = -\frac{1}{8}(x + 0.5)^2 + 2$$. 9. Input all these equations into Desmos or GeoGebra as they are to visualize the butterfly shape. 10. Adjust parameters such as the horizontal shifts and coefficients to customize the shape and size of the wings as needed. Final note: Combining these quadratic functions creates a butterfly shape through their parabolic curves.