1. **Stating the problem:** We start with the curve given by the equation $y = -x^2$. We want to shift this curve so that its axis of symmetry moves from $x=0$ to $x=-1$ and its orthogonal axis (vertex line) moves from $y=0$ to $y=3$. 2. **Understanding the original curve:** The original curve $y = -x^2$ is a parabola opening downward with vertex at $(0,0)$ and axis of symmetry $x=0$. 3. **Formula for shifting a parabola:** To shift the parabola horizontally by $h$ units and vertically by $k$ units, we replace $x$ by $(x - h)$ and $y$ by $(y - k)$ in the original equation. The new equation becomes: $$y - k = - (x - h)^2$$ 4. **Applying the shifts:** Here, the axis of symmetry moves from $x=0$ to $x=-1$, so the horizontal shift is $h = -1$. The orthogonal axis moves from $y=0$ to $y=3$, so the vertical shift is $k = 3$. 5. **Substitute $h$ and $k$ into the formula:** $$y - 3 = - (x - (-1))^2$$ $$y - 3 = - (x + 1)^2$$ 6. **Simplify the equation:** $$y = - (x + 1)^2 + 3$$ 7. **Final answer:** The equation of the new curve after shifting is: $$\boxed{y = - (x + 1)^2 + 3}$$