A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=72t-16t^2. What is the maximum height that the ball will reach?Do not round your answer

Answer:The maximum height that the ball will reach is 81 ftStep-by-step explanation:Note that the tray of the ball is given by the equation of a parabola of negative main coefficient. Then, the maximum value for a parabola is at its vertex.For an equation of the form[tex]at ^ 2 + bt + c[/tex]Sothe t coordinate of the vertice is:[tex]t =-\frac{b}{2a}[/tex]In this case the equation is:[tex]h(t)=72t-16t^2[/tex]So[tex]a=-16\\b=72\\c=0[/tex]Therefore[tex]t =-\frac{72}{2(-16)}[/tex][tex]t=2.25\ s[/tex]Finally the maximum height that the ball will reach is[tex]h(2.25)=72(2.25)-16(2.25)^2[/tex][tex]h=81\ ft[/tex]