1. **State the problem:** We are given the function $h = -0.5d(d-24)$ which describes a parabola. We want to understand its shape, vertex, and intercepts. 2. **Rewrite the function:** Expand the expression: $$h = -0.5d(d-24) = -0.5(d^2 - 24d) = -0.5d^2 + 12d$$ 3. **Identify the parabola type:** Since the coefficient of $d^2$ is negative ($-0.5$), the parabola opens downward. 4. **Find the vertex:** The vertex of a parabola $h = ad^2 + bd + c$ is at $d = -\frac{b}{2a}$. Here, $a = -0.5$, $b = 12$, so $$d = -\frac{12}{2 \times -0.5} = -\frac{12}{-1} = 12$$ 5. **Calculate the maximum height $h$ at $d=12$:** $$h = -0.5(12)^2 + 12(12) = -0.5(144) + 144 = -72 + 144 = 72$$ 6. **Find the intercepts:** - When $d=0$, $h = -0.5 \times 0 \times (0-24) = 0$ - When $h=0$, solve $-0.5d(d-24) = 0$ which gives $d=0$ or $d=24$ 7. **Summary:** The parabola starts at $(0,0)$, reaches a maximum height of 72 at $d=12$, and returns to zero at $d=24$. **Final answer:** The vertex is at $(12,72)$, and the parabola opens downward with zeros at $d=0$ and $d=24$.