I assume you start with the parent function f(x)=x² and you want to see how the parent morphs into the quadratic f(x)=-⅓x²-3. So look at f(x)=-x². This inverts the parabola f(x)=x², which is U-shaped with its vertex at the origin. The vertex doesn’t change but the parabola becomes inverted and the vertex is a maximum rather than a minimum point.
Now we add the coefficient ⅓ so we have f(x)=-⅓x². The coefficient controls the spread or width of the parabola. Consider x=3. The parent has a value 9 but the function f(x)=⅓x² reduces the value to 3, which squashes the parabola vertically making it look wider. And f(x)=-⅓x² has the same effect but, since the parabola is inverted, it is squashed from the negative direction, a reflection of f(x)=⅓x² in the x-axis.
Finally, the constant -3 shifts the vertex down 3 units so it’s under the x-axis, sliding down the y-axis to (0,-3).
The complete transformation is invert, broaden, shift down.