Question

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function h = –16t^2 + 36t + 10
a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary.
b. What is the ball's maximum height?

Answer 1

So hhmm notice the picture below

thus, the vertex of any parabola is

$\bf \qquad \textit{vertex of a parabola}\\ \quad \\ \begin{array}{lccclll} h=&-16t^2&+36t&+10\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)$

so, it reaches its maximum point at $\bf -\cfrac{{{ b}}}{2{{ a}}}\quad seconds$

and the ball's' maximum height is $\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\quad feet$