2. The moving point problem of general quadratic function is the combination of linear function and quadratic function, and the key is to connect the related moving point with the expression of function. Because you didn't give a specific question here, let me sum it up. Many of them find the maximum or minimum value of a line segment composed of a point in each of two functions. In fact, just add or subtract the expressions of two functions, and then get a new quadratic function expression, and find the maximum value of the new quadratic function. To do this kind of problem, we must first lay a good foundation, and then we must find some questions to do, and summarize and reflect in the process of doing it. You'll get better after training for a while.
3. Coordinates are integers, and the distance from this point to the origin is just like the length of two hypotenuses whose right angles are integers. Many of them have roots, which is normal. For example, the distance from point (2,2) to the origin is 2√2. The distance from point (2,3) to the origin is √ 13.