Geometrically, a parabola is the set of all points in the plane which are equally distant from a fixed point, called the focus, and a fixed line, called the directrix. We will say more about this geometric definition below. Algebraically, a parabola is the graph, in the x-y coordinate system, of an equation of the form y=ax²+bx+c. Such equations define functions called "quadratic" functions. The simplest of all quadratic functions is defined by y=x^*2. This function's graph is the parabola with it's lowest point, the vertex, at the origin and which is symmetric to the y-axis. It passes through the set of points of the form (a,a²); in other words, the second coordinate of any point on this parabola is the square of the first coordinate. All other parabolas can be generated from the y=x² parabola with some combination of translations, reflections...