1. **State the problem:** We are given a projectile's altitude function $h(t)$ with points $(0,5)$, $(12,19.4)$, and $(25.93,0)$, and asked which statement about the projectile's motion is true. 2. **Analyze the given points:** - At $t=0$, $h(0)=5$, so the projectile starts at 5 feet above the ground, not from the ground. - At $t=12$, $h(12)=19.4$, which is the highest point (vertex) of the parabola, so the maximum altitude is 19.4 feet. - At $t=25.93$, $h(25.93)=0$, meaning the projectile hits the ground at this time. 3. **Check each statement:** - "The projectile reaches a maximum altitude of 12 feet." This is false because the maximum altitude is 19.4 feet. - "The projectile reaches its maximum altitude after 12 seconds of flight." This is true since the vertex is at $t=12$. - "The projectile is launched from the ground." This is false because it starts at 5 feet. - "The altitude of the projectile is increasing on the interval $5 < t < 20$." This is false because the altitude increases until $t=12$ and then decreases after $t=12$. 4. **Conclusion:** The true statement is: **The projectile reaches its maximum altitude after 12 seconds of flight.**