
Patrick B. answered 02/13/19
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The parabola is y = ax^2 + bx + C where
(s,t) and (m,n) are the points on the parabola with y-intercept (0,C)
Then
t = as^2 + bs + C
n = am^2 + bm + C
is a 2x2 that can be solved by substitution or elimination.