Question

Which line will have no solution with the parabola y – x + 2 = x2? y = –3x –3 y = –2x –3 y = 2x –3 y = 3x –3

Answer 1

Try this option:
the line y=-2x-3.
Explanation:
if to see the pair of equations: y=x²+x-2 and y=-3x-3, ⇔ x²+x-2=-3x-3, ⇔ x²+4x+1=0, D>0, then they have two common points.
if to see the pair of equations: y=x²+x-2 and y=-2x-3, ⇔ x²+3x+1=0, ⇒D>0, then they have two common points.
for y=x²+x-2 and y=2x-3: x²+x+1=0, D<0, it means, that these equations have no common points.
for y=x²+x-2 and y=3x-3: x²-2x+1=0, D=0, it means, that these equations have the only common point.

answer: y=2x-3.