On the attached diagram red curve is the graph of the quadratic function [tex]y = 2(x - 2)^2 + 2.[/tex] As you can see this graph has no intersections with x-axis, this means that there are no solutions.
If you translate red curve 2 units down, you obtaine the graph (blue curve) of the function [tex]y = 2(x - 2)^2[/tex] and this graph has one common point with x-axis. This means that there will be exactly one solution.
Answer: k=-2 (you add -2 to the function [tex]y = 2(x - 2)^2 + 2[/tex] to obtain the function [tex]y = 2(x - 2)^2[/tex]).
