Question

for context, the equation for rocket one is h=-16t^2+150t+1 and rocket 2 starts at 0, has the peak of 600 in 6 seconds and in 12 seconds. i would like to know what the vertex is

Answer 1

$\begin{gathered} \text{For Rocket 1} \\ \text{The vertex is the highest distance from the ground } \\ h=-16t^2+150t+1 \\ \text{vertex =(}\frac{-b}{2a},h(\frac{-b}{2a})\text{)} \\ a=-16 \\ b=150 \\ \frac{-b}{2a}=\frac{-150}{2(-16)}=\frac{-150}{-32}=4.6875 \\ h=-16(4.6875)^2+150(4.6875)+1 \\ h=352.6 \\ \text{hence the highest point for rocket 1 is 352.6 ft} \\ \text{For rocket 2} \\ \text{From the graph the highest point is almost 600ft, th}\operatorname{erf}ore\text{ } \\ \text{the rocket that flew }higher\text{ was rocket 2} \end{gathered}$