Question

When a cannonball is fired, the equation of its pathway can be modeled by h = -16t² + 128t. Find the maximum height of the cannonball

Answer 1

h = 4ft per second it carries

Answer 2

so hmmm check the picture below

the leading term's coefficient for that quadratic is negative, meaning is opening downwards

so.. hmm where's the vertex anyway? well


`\bf \textit{vertex of a parabola}\\ \quad \\ h=-16t^2+128t\\\\\\ \begin{array}{lccclll} h=&-16t^2&+128t&+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,the cannonball reaches a maximum height of
`\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}`