Answer:
The maximum height of soccer ball is 12.25 ft.
Step-by-step explanation:
It is given that Tiffany kicks a soccer ball off the ground and in the air, with an initial velocity of 28 feet per second. It means v = 28 ft.
Given formula is
\(H(t)=-16t^2+vt+s\)
The initial height of ball is 0.
\(H(0)=-16(0)^2+v(0)+s\)
\(0=s\)
The height of ball defined by the function
\(H(t)=-16t^2+(28)t+0\)
\(H(t)=-16t^2+28t\)
It is a downward parabola and the vertex of a downward parabola is the point of maxima.
The vertex of a parabola \(f(x)=ax^2+bx+c\) is
\((\frac{-b}{2a},f(\frac{-b}{2a}))\)
\(\frac{-b}{2a}=\frac{-28}{2(-16)}=0.875\)
\(H(0.875)=-16(0.875)^2+28(0.875)=12.25\)
Therefore the maximum height of soccer ball is 12.25 ft.
