Hi! There are multiple methods, but one I see a lot is using three points on the graph of the parabola. The equation of a parabola is y=ax^2+bx+c. You can plug the coordinates from the three points into that equation for x and y, and you'll end up with a 3-variable system where a, b, and c are the variables. You can solve the system for a, b, and c and then put those values into the equation y=ax^2+bx+c. I've done an example below. If you need help solving 3-variable systems, there is a video on it here: https://www.khanacademy.org/math/algebra-home/alg-system-of-equations/alg-systems-with-three-variables/v/systems-of-three-variables-2 

Another method you can use is using the parabola's focus and directrix. There's a video on that here: https://www.khanacademy.org/math/algebra2/intro-to-conics-alg2/focus-and-directrix-of-a-parabola-alg2/v/equation-for-parabola-from-focus-and-directrix 

This was a cool question. Hope this helped!