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Of course not! There's a whole x-y Cartesian plane out there to play on, so there's no reason they should be. They can be tilted and positioned any which way. Of course, when you start out learning about conic sections (including parabolas), you start with the simplest parabola, y = x^2, then graduate to (y-b) = (x-a)^2 and similar forms interchanging x and y. And when you use parabolas, to figure the trajectory of an object which was launched with a certain velocity, in a certain direction, and is subject to gravity, you use only untilted parabolas (well, parabolae, if you want to use the correct plural word). Most algebra classes don't have you figure out what a tilted parabola equation would look like, but it isn't that tough to figure out. First, though, it helps to reconsider just what it is that you do when you graph a point on the curve of an equation (and you thought you knew!). Let's say you're working with an ordinary function on ordinary x-y axes (it could be a parabola... read more

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