Question

A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = -16t2 + 704t. After how many seconds does the projectile take to reach its maximum height? Show your work for full credit

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Answer 1

check the picture below

so the maximum height happens at the vertex for f(x) and happens after "x" seconds


`\bf \textit{vertex of a parabola}\\ \quad \\ \begin{array}{lccclll} h(t)=&-16t^2&+704t&+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 projectile took
`\bf -\cfrac{{{ b}}}{2{{ a}}}\quad seconds`