Find the formula for the parabola that passes through the points (2,2) and (5,7) whose graph is given below:

Since (2,2) is the vertex, could I put this in vertex form y= (x-h)^{2}+k for (x-2)^{2}+2? I'm not sure how to incorporate the (5,7) point in though.

and

Finding the equation for a line that goes through a parabola, with the parabola's equation being y = x^{2}+ 2

I'm not sure where to even begin with this one. All the variables are throwing me off