Question 605082
I can put any number I want in for {{{x}}}, (+) or (-),
and I still get out {{{y}}}'s, so the domain is + infinity
to - infinity
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The curve is a parabola with a minimum at it's vertex, and
the vertex is at {{{ x = -b/(2a) }}} where
{{{ a = 3 }}}
{{{ b = 23 }}}
Vertex is at {{{ x = -23/(2*3) }}}
{{{ x = -23/6 }}}
Plug this into equation to find {{{ f(x) }}}
{{{ f(-23/6) = 3*(-23/6)^2 + 23*(-23/6) - 14 }}}
{{{ f(-23/6) = 529/12 - 529/6 - 84/6 }}}
{{{ f(-23/6) = -529/12 - 168/12 }}}
{{{ f(-23/6) = -697/12 }}}
So, the range is + infinity to -697/12 
Here's the plot:
{{{ graph( 400, 400, -12, 12, -60, 20, 3x^2 + 23x - 14 ) }}}