Question

An object is thrown upward with an initial velocity of 32 feet per second. The objects height is modeled by the function h(t) = - 16t2 + 32t where t is the time of the at height, h(t). What is the maximum height of the object?

32 ft
60 ft
72 ft
104 ft

Answer 1

check the picture below.


`\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} y = &{{ -16}}x^2&{{ +32}}x&{{ +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 object reaches at maximum height of
`\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\ feet`