here's my question :
Construct an example of a polynomial so that its graph goes through the points
If you want a quadratic, this is how to do it:
Pick one of the points as the vertex -- though it does matter which one you pick, because you get different answers otherwise, the problem is only asking for an example. Let's pick (3, -2).
The vertex form of the parabola is
Plug in the vertex for (h, k):
Plug in the other point for (x, y) to solve for a:
So the equation of the parabola would be