Question

Pablo and max's follows a flight pattern approximatley modled by the equation h(t)=-8t^2+16t+2 where h(t)is their rocket's height in meters t seconds after launch. How many seconds after the launch did their rocket reach it maximum height?

Answer 1

Check the picture below.

so from the picture below, we can see that the rock reach its maximum at the vertex of the parabolic path, now , let's get the x-coordinate then

`\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-8}x^2\stackrel{\stackrel{b}{\downarrow }}{+16}x\stackrel{\stackrel{c}{\downarrow }}{+2} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)`

`\left(-\cfrac{ 16}{2(-8)}~~~~ ,~~~~ 2-\cfrac{ (16)^2}{4(-8)}\right) \implies \left( - \cfrac{ 16 }{ -16 }~~,~~2 - \cfrac{ 256 }{ -32 } \right) \\\\\\ \left( 1 ~~~~ ,~~~~ 2 +8 \right)\implies \stackrel{ seconds ~~ meters }{(\text{\LARGE 1}~~,~~10)}`