What is a shadow generating function. How can you derive it.

for example,

Y1 = aX^2 + bX + c
Y2 = -1(aX^2 +bx + c) ... ( shares the same vertex with Y1, but has opposite concavity .. shadow Function)

express Y2 in terms of Y1 & Ym where Ym is the Shadow Generating Function.

Question

What is a shadow generating function. How can you derive it.

for example,

Y1 = aX^2 + bX + c
Y2 = -1(aX^2 +bx + c) ... ( shares the same vertex with Y1, but has opposite concavity .. shadow Function)

express Y2 in terms of Y1 & Ym where Ym is the Shadow Generating Function.

mertsj · Answer

ym is the horizontal line between the two functions

anonymous · Answer

yes.. thats on the given graph.  so do that mean that Ym = bx+c ??

what is How do that makes it an Shadow Generating fucntion?? or am i missing something here??

Also, How do i express Y2 in terms of Ym & Y1 ??

mertsj · Answer

Well I can't see the "given graph"

mertsj · Answer

But the y coordinate of the vertex is ym so I would write y2 in vertex form using the common vertex which would include ym

mertsj · Answer

The shadow function would be y=(4ac-b^2)/4a  since that is the y coordinate of the vertex.