What is shadow generating function?
y1 = (x-3)^2 + 16 has complex roots 3 +- i4; concave up with vertex (3,4)
where it exists another 'shadow function' which concaves down and share the same vertex (3,4) but with real roots x=3 +- 4. This shows real roots are helpful to find the imaginary root of it's corresponding concave up function.
When y1 = (x+2) (x-(3+2i)) (x- (3-2i) ) ,
1. what is the shadow function y2 given that y2 shares two points with y1 ?
2. Express y2 in terms of y1 and ym where ym is called the 'shadow generation function'
3. How can this be applied to quartics?

Question

What is shadow generating function?
y1 = (x-3)^2 + 16 has complex roots 3 +- i4; concave up with vertex (3,4)
where it exists another 'shadow function' which concaves down and share the same vertex (3,4) but with real roots x=3 +- 4. This shows real roots are helpful to find the imaginary root of it's corresponding concave up function. 
When y1 = (x+2) (x-(3+2i)) (x- (3-2i) ) ,
1. what is the shadow function y2 given that y2 shares two points with y1 ?
2. Express y2 in terms of y1 and ym where ym is called the 'shadow generation function'
3. How can this be applied to quartics?