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.

anonymous · Answer

anonymous · Answer

So, shadow of $(x - a)^2 + b$ is $-(x - a)^2 + b$

anonymous · Answer

and what about the 'ym' which is the shadow generating function?

anonymous · Answer

I don't understand.

anonymous · Answer

Do you mean for any order polynomial?

anonymous · Answer

okk let me send u the whole sheet so u can have a look at it ?

anonymous · Answer

anonymous · Answer

For cubics it's rather interesting, I have to think about it.

anonymous · Answer

plzzzz sir and if u find any solution just let me know and it would be great of u sir if u send me a mssg?

mathteacher1729 · Answer

This is an interesting problem, I've seen it for quadratics, but not cubics.