Question

A ball is thrown into the air. The height in feet of the ball can be modeled by the equation h = -16t2 + 20t + 6 where t is the time in seconds, the ball is in the air. When will the ball hit the ground? How high will the ball go?

Answer 1

`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`

`√(Δ)=√(784)=28`

max:

`p=-(b)/(2a)=-(20)/(-32)=(20)/(32)=(5)/(8)`

max heigh:
`h=-16((5)/(8))^2+20*(5)/(8)+6=-16(25)/(64)+(100)/(8)+6`

`h=-(25)/(4)+(50)/(4)+6=(-25+50+24)/(4)=(49)/(4)`

`h=(49)/(4)` at
`t=(5)/(8)s`

will fall down at t:

`t=(-20-28)/(-32)=(-48)/(-32)=(3)/(2)=1.5`

`t=1.5s`