Question 831159
Look at the discriminant,
{{{D=2^2-4(2)(m+4)}}}
{{{D=4-8m-32}}}
{{{D=-8m-28
a) Two real solutions, {{{D>0}}}
{{{-8m-28>0}}}
{{{-8m>28}}}
{{{m<-7/2}}}
b) One real solution, {{{D=0}}}
{{{-8m-28=0}}}
{{{m=-7/2}}}
c) No real solutions, {{{D<0}}}
{{{-8m-28<0}}}
{{{m>-7/2}}}
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Three examples graphed with {{{m=-8}}}(Red), {{{m=-7/2}}}(Green) and {{{m=0}}}(Blue).
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{{{ graph( 300, 300, -10, 10, -10, 10, 2x^2+2x+(-8+4),2x^2+2x+(-7/2+4),2x^2+2x+(0+4)) }}}