Question 366783
{{{-2x^2 - x + 15}}}
Find the roots, which are the x-axis crossings.
Use quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{a = -2}}}
{{{b = -1}}}
{{{c = 15}}}
{{{x = (-(-1) +- sqrt( (-1)^2-4*(-2)*15 ))/(2*(-2)) }}} 
{{{x = ( 1 +- sqrt( 1 + 120 ))/ -4 }}}
{{{x = (1 + 11)/-4}}}
{{{x = -3}}}
and
{{{x = (1 - 11)/-4}}}
{{{x = 5/2}}}
The difference between the roots is {{{5/2 - (-3) = 11/2}}}
Here's the plot:
{{{ graph( 400, 400, -5, 5, -5, 20, -2x^2 - x + 15) }}}