1.1. Given that ${x}^{3}-8{x}^{2}+16x=x(x-4{)}^{2}$

Sketch the graph of $y={x}^{3}-8{x}^{2}+16x+3$ , showing clearly the coordinates of the points where the curve crosses the coordinate axes and the co-ordinates of any minimum points. (You do not need to state the co-ordinates of any maximum points).

1.2. The graph with equation   $y+a={x}^{3}-8{x}^{2}+16x$  crosses the $x$-axis three times.  Find the range of possible values of $a$.