the simplest polinomial is
x squared

then the lowest by your definition would be:
p(x) x squared + 1

make x = 1

P(1) = 1 squared + 1
P(2) = 2 squared + 1
= 5

this maybe wrong.

p.s how do u post a graph (i have a problem but i don't know how to post a graph to ask the question) (its polynomial numbers)