Question 1137661
{{{ t = 0 }}} is when bag is dropped
{{{ h(0) = -5*0^2 + 80 }}}
{{{ h(0) = 80 }}} m
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{{{ h(t) = 0 }}} is height when bag hits ground
{{{ 0 = -5t^2 + 80 }}}
{{{ 5t^2 = 80 }}}
{{{ t^2 = 16 }}}
{{{ t = 4 }}} s
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(a)
The domain is {{{ 0 }}} sec to {{{ 4 }}} sec
The range is {{{ 0 }}} m to {{{ 80 }}} m
(b)
{{{ graph( 400, 400, -1, 5, -10, 100, -5x^2 + 80 ) }}}
( with above restrictions )
c
{{{ h = -5*t^2 + 80 }}}
{{{ 5t^2 = -h + 80 }}}
{{{ t^2 = ( 80 - h )/5 }}}
{{{ t(h) = sqrt( ( 80 - h )/5 ) }}}
{{{ graph( 400, 400, -2, 100, -5, 5, +sqrt( ( 80 - x )/5 ), -sqrt( ( 80 - x )/5 ) ) }}}
(d)
The inverse is not a function, since there are
2 values for {{{ t(h) }}} for every {{{ h }}}