Question 1063607
If they did intersect, you would equate the two expressions for y:


{{{x^2+3x-5=2x+b}}}
{{{x^2+3x-2x-5-b=0}}}
{{{x^2+x-(b+5)=0}}}


Since you DO NOT want the line and parabola to intersect, then you want this equation to have NO REAL SOLUTIONS, and you must have the discriminant be negative.



{{{1^2-4*1*(-1(b+5))<0}}}


{{{1+4(b+5)<0}}}


{{{1+4b+20<0}}}


{{{4b<-21}}}


{{{highlight(b<-21/4)}}}---------the requirement so that your given line and parabola do not intersect.