I call that point, point B, then I could say line This point right over there, is 2 centimeters from A. Start at A and I go 2 centimeters in that direction, My screen right over here, that are exactly 2Ĭentimeters away from A. And what I'm curious about is all of the points on (For instance, the four corners of a square cannot lie on any legitimate parabola no matter which way the directrix is facing.) Hope that wasn't too far afield for you! With this more flexible notion of what a parabola is, now it would generally take FOUR points to define the parabola, and there are a couple of extra exceptions beyond the fact that no three of them can be on a straight line. If you're okay with the line not being horizontal, then you're going to get shapes that aren't the graph of a function, but a circle isn't the graph of a function either because lots of vertical lines cross it in more than one point.
We talk about a parabola as being the locus of points that are the same distance from a given point and a given line, but nearly all the time we only consider the case when that line is horizontal. I don't want to get too weird, but parabolas are a little more complicated. Given any three points that aren't on the same line and with no two points on the same vertical line, there is exactly one quadratic function whose graph passes though those three points.
The rules for quadratic functions are the same as the rules for circles.
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