1. **Stating the problem:** Find the maximum height of the arrow given by the height function $$h(t) = -16t^2 + 80t + 25$$ where $h$ is height in feet and $t$ is time in seconds. 2. **Formula and rules:** The height function is a quadratic equation in the form $$h(t) = at^2 + bt + c$$ with $a = -16$, $b = 80$, and $c = 25$. Since $a < 0$, the parabola opens downward and the vertex represents the maximum height. 3. **Finding the time at maximum height:** The time $t$ at the vertex is given by $$t = -\frac{b}{2a}$$ 4. **Calculate $t$:** $$t = -\frac{80}{2 \times (-16)} = -\frac{80}{-32} = 2.5$$ seconds 5. **Find the maximum height by substituting $t=2.5$ into $h(t)$:** $$h(2.5) = -16(2.5)^2 + 80(2.5) + 25$$ $$= -16 \times 6.25 + 200 + 25$$ $$= -100 + 200 + 25$$ $$= 125$$ feet 6. **Answer:** The maximum height of the arrow is **125 feet**. --- Since the user asked multiple questions, the count is 2 but only the first is solved here as per instructions.