Question 184401
The graph crosses the x-axis wherever {{{y=0}}}
Set {{{y = o}}}
{{{2x^2 - 4x - 16 = 0}}}
Use quadratic formula with {{{ax^2 + bx + c = 0}}}
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 2}}}
{{{b = -4}}}
{{{c = -16}}}
{{{x = (-(-4) +- sqrt( (-4)^2-4*2*(-16) ))/(2*2) }}}
{{{x = (4 +- sqrt( 16 + 128 ))/4 }}}
{{{x = (4 +- sqrt( 144 ))/4 }}}
{{{x = (4 +- 12)/4 }}}
{{{x = (4 + 12)/4}}}
{{{x = 4}}}
and
{{{x = 4 - 12)/4}}}
{{{x = -2}}}
the graph crosses the x-axis at {{{x = -2}}} and {{{x = 4}}}
Here's a plot:
{{{ graph( 500, 500, -4, 7, -18, 4, 2x^2 - 4x - 16) }}}