1. The problem gives two functions: $$h(d) = - \frac{1}{9} (d - 4)^2 + 4$$ and $$h(d) = - \frac{1}{9} (d + 1)^2 + 4$$. We are asked to analyze these parabolas, which model the height of a basketball ball as a function of horizontal distance $d$. 2. Both functions are quadratic in vertex form: $$h(d) = a(d - h)^2 + k$$ where $(h,k)$ is the vertex and $a$ determines the parabola's opening direction and width. 3. For the first function, $$a = -\frac{1}{9}$$, vertex at $(4,4)$, so the parabola opens downward with maximum height 4 at $d=4$. 4. For the second function, $$a = -\frac{1}{9}$$, vertex at $(-1,4)$, also opening downward with maximum height 4 at $d=-1$. 5. The graph description matches the first function, showing a parabola opening downward with vertex at $(4,4)$. 6. The problem asks to confirm understanding and provide the answer for the first function. 7. The answer: The function $$h(d) = - \frac{1}{9} (d - 4)^2 + 4$$ models a basketball shot with maximum height 4 at horizontal distance 4. The parabola opens downward, indicating the ball rises then falls, reaching the hoop around $d=7$ as described.