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The Catenary and Parabola are different curves that look similar; they are both "U" shaped and symmetrical, increasing infinitely on both sides to a minimum.
An x2 parabola will always have one vertex, but depending on the discriminant of the function (b2-4ac) the parabola will either have 2 roots (it crosses the x-axis twice), 1 repeating root (the parabola meets the x-axis at a single point), or no real roots (the parabola doesn't meet the x-axis at all)
A parabola has no endpoints: it extends to infinity.A parabola has no endpoints: it extends to infinity.A parabola has no endpoints: it extends to infinity.A parabola has no endpoints: it extends to infinity.
To graph a parabola you must find the axis of symmetry, determine the focal distance and write the focal as a point, and find the directrix. These are all the main points you need to be able to draw a parabola.
Symmetrical. See http://www.orbitals.com for pictures of all the orbitals