1. **State the problem:** Given the quadratic function $$h = -0.2 d^2 + 0.8 d + 2,$$ find the value of $$h$$ at $$d = -1,$$ and determine the vertex of the parabola which represents the maximum height and its value. 2. **Calculate $$h$$ at $$d = -1$$:** Substitute $$d = -1$$ into the function: $$h = -0.2(-1)^2 + 0.8(-1) + 2 = -0.2(1) - 0.8 + 2 = -0.2 - 0.8 + 2 = 1.0$$ 3. **Find the vertex $$d$$-value (horizontal distance at max height):** For a parabola $$h = ad^2 + bd + c,$$ the $$d$$-coordinate of the vertex is given by: $$d = -\frac{b}{2a} = -\frac{0.8}{2 \times (-0.2)} = -\frac{0.8}{-0.4} = 2$$ 4. **Calculate the maximum height (vertex value):** Substitute $$d=2$$ into the function: $$h = -0.2(2)^2 + 0.8(2) + 2 = -0.2(4) + 1.6 + 2 = -0.8 + 1.6 + 2 = 2.8$$ 5. **Interpretation:** The height at $$d=-1$$ is $$h=1.0$$. The parabola reaches its maximum height of $$2.8$$ meters at $$d=2$$ meters. **Final answers:** - Height at $$d=-1$$: $$1.0$$ - Maximum height: $$2.8$$ at $$d=2$$