There must be minus sign with 4.9 .
[tex] h(t) = -4.9t^2+25t +80 [/tex]
The given equation is the equation of parabola , which is maximum at its vertex, and the formula of vertex is
[tex] t=-\frac{b}{2a}=-\frac{25}{2(-4.9)} = 2.55 seconds [/tex]
So the height is maximum at t=2.55 seconds and to find the maximum height , we need to plug 2.55 for t , that is
[tex] h(2.55)=-4.9(2.55)^2+25(2.55)+80 = Approx \ 112 \ m [/tex]
So the maximum height is 112 m .
