Put X=0 in parabola equation to find value of Y(point A) & do the same by putting Y=0 to get values of B,C. Then substitute in area of triangle equation & K turns out to be 0.25

Height of triangle = k (y when x = 0). Base of triangle = 2k (Put y=0 roots = ± k, base = distance from -k to k = 2k). Area = 0.5 * b * h = 0.5 * 2k * k = 1/8. Solving this we get k = sq root (0.125) = 0.35. So the answer should be 0.35

Y= 0 then roots will be root k and - root k ... so area of triangle is k* root k = 1/8 and hence ans is 0.25