  The Orlik-Solomon algebra is the cohomology ring of the complement of a
hyperplane arrangement A in C^n; it is the quotient of an exterior algebra E(V)
on |A| generators. Orlik and Terao introduced a commutative analog S(V)/I of
the Orlik-Solomon algebra to answer a question of Aomoto and showed the Hilbert
series depends only on the intersection lattice L(A). Motivated by topological
considerations, Falk and Randell introduced the property of 2-formality; we
study the relation between 2-formality and the Orlik-Terao algebra. Our main
result is a necessary and sufficient condition for 2-formality in terms of the
quadratic component I_2 of the Orlik-Terao ideal I: 2-formality is determined
by the tangent space T_p(V(I_2)) at a generic point p.
