Compare the orbit diagrams for the Logistic family f(x) = lamda*x(1-x) and for the Quadratic family f(x) = x^2+lamda. Do you see any similarities? Discuss them and point out the differences.

The orbit diagrams are the same shape, but that of f(x) = x^2 +l amda is a rotation of 180 degrees of the other orbit diagram.
 

What is the range of lamda values in the diagram for the Logistic family?

The lamda values are greater than or equal to 0.

What is the range of lamda values in the diagram for the Quadratic family?

The lamda values are less than or equal to 0. For lamda = 4, the graph of the Logistic map is special. The interval [0,1/2] is mapped entirely onto [0,1] twice.  This is not true for smaller (positive) values of lamda.

Find the value for lamda such that the graph of f(x) = x^2 + lamda covers the interval [-2,2] exactly twice, as described above for the Logistic map.

This occurs at lamda = -2.0.