A parabola with minimum at its vertex (−1,−3) intersects a parabola with maximum at its vertex (2,1) at exactly one point. If the leading coefficients of both parabolas have the same absolute value, then this absolute value can be written as PQ for positive integers P and Q with gcd(P,Q)=1. What is P+Q?
I know that the x value of the vertices is (-b/2a). We can plug that in, but I am still not sure how to find a, even after drawing 2 parabolas.