find the quadratic function whose vertex lies at the point -4,2 and passes through the points -2,6
The vertex is at (-4, 2), so you know this is a maximum or minimum point. Your next given point is (-2, 6), and this is obviously higher up on the graph than your vertex. This tells you that the vertex is a minimum for the graph.
y=$\displaystyle (x-b)^2+c$ will be your general equation where b is how much you move to the right (negative if you move to the left) and c is how far up you translate (negative if down).
So just use your vertex to move your graph, namely y=$\displaystyle (x+4)^2+2$