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?

so hhmm notice the picture below

thus, the vertex of any parabola is

[tex]\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)[/tex]

so, it reaches its maximum point at [tex]\bf -\cfrac{{{ b}}}{2{{ a}}}\quad seconds[/tex]

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

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?

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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?