Quadratic Functions

$f(x)$ and $g(x)$ are two quadratic polynomials: - $f(x) = Ax^2 + Bx + C$ - $g(x) = Dx^2 + Ex + F$ It is guaranteed that $f(x)$ and $g(x)$ do not intersect. That is, there is no real number $r$, such that $f(r) = g(r)$. You need to find a quadratic polynomial $h(x) = Px^2 + Qx + R$ such that the sum of areas under the curves $|f(x) - h(x)|$ and $|g(x) - h(x)|$ is minimized between integer points