Comets Have Elliptical Orbits, but the Orbits of Some Comets $y = a x ^ { 2 } + b x + c$

Essay

Comets have elliptical orbits, but the orbits of some comets are so vast that they are indistinguishable from parabolas. Find an equation of the form $y = a x ^ { 2 } + b x + c$ for the parabola that closely describes the orbit of the comet shown in the illustration.