The answer is "it depends". If you're only ever going to do examples of quadratic equations, then you can just store a, b and c. If you think you're going to do other types of equations, store the whole thing.
What really shouldn't be a consideration is that its a "waste" to store the full equation in the sense that you're wasting disk space. Unless you're storing millions of these things, don't worry about it. Disk is cheap.
Other viewpoints to take are YAGNI (Ya Ain't Gonna Need It) which would say to code with the situation you have now, quadratic equations, and don't worry about generalizing it. If you need to you can refactor the code and the data later.
Another way to look at it is KISS (Keep It Simple, Stupid). The simplest thing to do would likely to be to just store the complete equation. This makes retrieving the equation a simple database fetch, no code to generate the equation is necessary.
Personally, assuming you're not doing a huge amount of these things, I'd favor KISS in this situation. I wouldn't be confident that the system is only going to be used for quadratic equations. What you can do is make the system handle whatever equations but make the input form take a, b and c and turn that into a quadratic equation. If you need other equation types later, changing the input logic is much simpler than changing the data structure.