Parabol, The Fourth Eye

Level pending

For \(a² > 4b\), let the function \(S(a,b)\) be the area of the quadrilateral defined by four selected points of the parabola \(y =x²+ax+b\), respectively the y-axis interception, the first x-axis interception, the vertex and the second x-axis interception.

The value of the expression

\(\displaystyle \dfrac{S(-2,-4)}{S(2,-4)}\)

can be written as an irreducible fraction \(\dfrac{m}{n}\). Evaluate \(m+n\).


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