Question

h= 16t^2+80t+2016 Projectile Height. A rocket is fired upward from some initial distance above the ground. It's height in feet, h, above the ground, t seconds after it is fired, is given by.... what is the maximum height (in ft.)?

Answer 1

check the picture below, the maximum height occurs at the vertex

now  $\bf \begin{array}{lccclll} h=&-16t^2&+80t&+2016\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)$

so the maximum height is $\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\quad feet$