Question 264901
Subtract the 2nd equation from the 1st
{{{y = x^2 + 4x + 3}}}
{{{-y = -x - 1}}}
{{{0 = x^2 + 3x + 2}}}
Use the quadratic formula to find roots
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1}}}
{{{b = 3}}}
{{{c = 2}}}
{{{x = (-3 +- sqrt( 3^2-4*1*2 ))/(2*1) }}}
{{{x = (-3 +- sqrt( 9 - 8 ))/2 }}}
{{{x = (-3+1)/2}}}
{{{x = -1}}}
and
{{{x = (-3-1)/2}}}
{{{x = -2}}}
The points I have so far are
(-1,?) and (-2,?)
To find y-components, plug x's back into original equatiuon
{{{y = x^2 + 4x + 3}}}
{{{y = (-1)^2 + 4*(-1) + 3}}}
{{{y = 1 - 4 + 3}}}
{{{y = 0}}}
I have point (-1,0) now
and
{{{y = x^2 + 4x + 3}}}
{{{y = (-2)^2 + 4*(-2) + 3}}}
{{{y = 4 - 8 + 3}}}
{{{y = -1}}}
The other point is (-2,-1)
I'll plot them to check answers
{{{ graph( 500, 500, -6, 6, -6, 6, x^2 + 4x + 3,x + 1) }}}