1) with the 3 coordinates and the local max & min, that gives you 5 conditions, so you can try a quartic equation ax^4+bx^3+cx^2+dx+e=y
substitute the coordinates, and note that between -4 and 2, the first derivative is 0 and the second is negative. You can choose whatever point you want. Same thing for the point between 2 and 4.
2) substitute the coordinates (-4,0) and (0,2) into a(x-h)^2+k and note that the minimum is attained at -4, so f'(-4)=0 and f''(-4)>0.