Recover the curve from its range and count line intersections

$C:y=(-2x^2-2x+a)/(x+1)$, where a is a non-zero constant. C exists for y≤−2 or y≥b, where b is positive.

(i) Using an analytical method, show a=−2 and hence find b.5 marks

(ii) Sketch C, clearly showing turning-point coordinates and asymptotes.3 marks

(iii) Show(−3,6) lies on y=px+3 p+6 for every real p. Hence use the sketch in(ii) to find p for which $px+3p+6=(-2x^2-2x-2)/(x+1)$ has two distinct real roots.2 marks