The question is not clear. Do you want to form quadratic equation in general form. In that case

let the quadratic equation be y = ax^2+ bx + c. Now the points ( 0,189 ) lies on it so we get c = 189

now we have y = ax^2 + bx + 189; the points ( 116,0) and ( -116,0) lie on it. thus we get

( 116)^2 a + 116 b + 189 = 0 and

(116)^2 - 116 b + 189 = 0

Solve these two equations for a and b.