  A remarkable connection between the order of a maximum clique and the
Graph-Lagrangian of a graph was established by Motzkin and Straus in 1965. This
connection and its extension were useful in both combinatorics and
optimization. Since then, Graph-Lagrangian has been a useful tool in extremal
combinatorics. In this paper, we give a parametrized Graph-Lagrangian for
non-uniform hypergraphs and provide several Motzkin-Straus type results for
nonuniform hypergraphs which generalize results from [1] and [2]. Another part
of the paper concerns a long-standing conjecture of Frankl-F\"uredi on
Graph-Lagrangians of hypergraphs. We show the connection between the
Graph-Lagrangian of $\{1, r_1, r_2, \cdots, r_l\}$-hypergraphs and $\{ r_1,
r_2, \cdots, r_l\}$-hypergraphs. Some of our results provide solutions to the
maximum value of a class of polynomial functions over the standard simplex of
the Euclidean space.
