Answer:
69 feet
Step-by-step explanation:
we have
[tex]h(t)=-16t^{2}+64t+5[/tex]
where
h(t) is the height of the ball
t is the time in seconds
we know that the given equation is a vertical parabola open downward
The vertex is the maximum
so
the y-coordinate of the vertex represent the maximum height of the ball
Convert the quadratic equation into vertex form
The equation in vertex form is equal to
[tex]y=(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
[tex]h(t)=-16t^{2}+64t+5[/tex]
[tex]h(t)-5=-16t^{2}+64t[/tex]
[tex]h(t)-5=-16(t^{2}-4t)[/tex]
[tex]h(t)-5-64=-16(t^{2}-4t+4)[/tex]
[tex]h(t)-69=-16(t^{2}-4t+4)[/tex]
[tex]h(t)-69=-16(t-2)^{2}[/tex]
[tex]h(t)=-16(t-2)^{2}+69[/tex]
the vertex is the point (2,69)
therefore
The maximum height is 69 ft
