Question 1011968
The domain (possible t values) must be greater than zero
because t is time of the stone in air and in this case
negative time has no meaning.
The stone will be thrown and will hit the ground again, 
and time in air will again be meaningless. The stone will 
hit the ground when the height (h(t)) is zero again so:
.
{{{h(t)=20t-5t^2}}}
. 
When h(t)=0:
{{{0=20t-5t^2}}}
{{{0=(t)(20-5t)}}}
{{{t=0}}} {{{OR}}} {{{20-5t=0}}}
{{{t=0}}} {{{OR}}} {{{20=5t}}}
{{{t=0}}} {{{OR}}} {{{4=t}}}
.
So the only valid times when the rock is in the air are between
t=0 (when the stone is thrown) and t=4 (when the stone lands).
Any other values give a negative height.