Point of order--"domain", "range", and "inverse" are things associated with functions, whereas a "parabola" is a shape. You need to find the domain, range, and inverse of a quadratic function, the graph of which is a parabola. Step one, then, could be to find the quadratic equation in question explicitly. Are you familiar with the "vertex form" of a quadratic equation? That would be the easiest way to start, since the coordinates of the vertex appear in the equation, and you know what those are. After that, here are the questions that you want to ask yourself: Are there any values of x that cannot be plugged into this equation? If there are, those are numbers which are not in the domain. Everything else will be (and that could mean that the domain is "everything"). What values of y can I get out of this equation? Try some different values of x and see what you get if the answer to this doesn't jump out at you. All the different possible y's that you can get are in the range. (Once you have answered those questions, take a look at the parabola itself. There are geometric reasons for those answers as well. There is a way to just look at the graph and know what the domain and range are. But it's easier to see that with the answer in hand.) The inverse is a harder question to figure out. This quadratic equation won't be invertible. Every value of y will have two "preimages". If you restrict the domain artificially you could get an inverse. Answer from InfanticideAquifer on reddit.com