Question

A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = -16t2 + 640t. After how many seconds does the projectile take to reach its maximum height? Show your work for full credit.

Answer 1

so hmm  notice the picture below

it happened after "x" seconds

now  $\bf \textit{vertex of a parabola}\\ \quad \\ \begin{array}{lcclll} h(t) = &-16t^2 &+ 640t+&0\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)$

so it was after $\bf -\cfrac{{{ b}}}{2{{ a}}}$ seconds