If you want to find function `f` whose graph goes through a point `(x,y)`. That means you need to find solution of equation `f(x)=y`. If you have several points that means you need to find solution of system of equations.
In your case you want to find polynomial `f(x)=ax^4+bx^3+cx^2+dx+e` and for that you need to solve the following system:
Now you have system of 5 linear equations with 5 variables which you can solve by using Gauss elimination or some other method. Solution to this system of equations is
`a=-2`, `b=3`, `c=3`, `d=4`, `e=10`
Hence, your polynomial is: