Question

In the system of equations shown, c is an integer. for what minimum value of c does the system have exactly two distinct solutions

y=3(x-1)^2 +4
y=-2(x-1)^2 + c

Answer 1

The minimum value of c such that the system has exactly two distinct solutions is 4. When c=4, the two parabolic equations intersect at exactly two points (1, 4) and (x, y), which are the two distinct solutions.