\(f(t)=h=-16t^2+20t+6\)
a=-16, b=20, c =6
Δ=\(b^2-4ac=20^2-4*(-16)*6=400+384=784\)
\(\sqrt{Δ}=\sqrt{784}=28\)
max:
\(p=-\frac{b}{2a}=-\frac{20}{-32}=\frac{20}{32}=\frac{5}{8}\)
max heigh: \(h=-16(\frac{5}{8})^2+20*\frac{5}{8}+6=-16\frac{25}{64}+\frac{100}{8}+6\)
\(h=-\frac{25}{4}+\frac{50}{4}+6=\frac{-25+50+24}{4}=\frac{49}{4}\)
\(h=\frac{49}{4}\) at \(t=\frac{5}{8}s\)
will fall down at t:
\(t=\frac{-20-28}{-32}=\frac{-48}{-32}=\frac{3}{2}=1.5\)
\(t=1.5s\)
