Your biologist friend is investigating the shape of a plant structure.

It can be modeled as a surface whose cross-section parallel to theyz-plane is a cosine function (i.e. as a function of y withx fixed), and whose cross-section parallel to thexz-plane is a quadratic function (i.e. as a function ofxwithyfixed).

(a) Find a surfacef(x,y) which is a possible model for the plant structure. Explain how your answer fits the requirements of the biologist.