Question 1057359
{{{ h(x) = -5x^2 + 7x + 3 }}}
The rocket is launched at {{{ x = 0 }}}
so, {{{ h(0) }}} gives you the height the
rocket was launched from
{{{ h(0) = -5*0^2 + 7*0 + 3 }}}
{{{ h(0) = 3 }}}
Height at launch time was 3 m
------------------------------
The x-value of the vertex {{{ h[max] }}} is
given by the formula:
{{{ x[max] = -b/(2a) }}}, where
{{{ a = -5 }}}
{{{ b = 7 }}}
-----------------
{{{ x[max] = -7/(2*(-5)) }}}
{{{ x[max] = 7/10 }}}
Plug this value back into equation to
find {{{ h[max] }}}
{{{ h[max] = -5*(7/10)^2 + 7*(7/10) + 3 }}}
{{{ h[max] = -5*(49/100) + 49/10 + 60/20 }}}
{{{ h[max] = -49/20 + 98/20 + 60/20 }}}
{{{ h[max] = 109/20 }}}
{{{ h[max] = 5.45 }}} m
The max height is 5.45 m
This is only 2.45 m above launch height. 
Something seems wrong. I think the {{{ 7x }}}
term should be a lot bigger.
-------------------------------
The time when the rocket reaches max height 
is the 7/10 sec
-------------------
The rocket hits the ground when {{{ h(x) = 0 }}}
( zero height )
{{{ -5x^2 + 7x + 3 = 0 }}}
Use the quadratic formula
{{{ x = ( -b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = -5 }}}
{{{ b = 7 }}}
{{{ c = 3 }}}
{{{ x = ( -7 +- sqrt( 7^2-4*(-5)*3 ))/(2*(-5)) }}}
{{{ x = ( -7 +- sqrt( 49 + 60 ))/(-10) }}}
{{{ x = ( -7 +-sqrt( 109 )) / (-10) }}}
{{{ x = ( -7 - 10.44 ) / (-10) }}}
{{{ x = 17.44 / 10 }}}
{{{ x = 1.744 }}}
In 1.744 sec the rocket hits the ground
--------------------------------------
Here's the plot of the equation:
{{{ graph( 400, 400, -1, 3, -1, 7, -5x^2 + 7x + 3 ) }}}
This doesn't look like the flight of a "rocket". Check
your data and my math ( I think my math is OK )