  It has long been known that the quadratic term in the degree of the colored
Jones polynomial of a knot is bounded above in terms of the crossing number of
the knot. We show that this bound is sharp if and only if the knot is adequate.
  As an application of our result we determine the crossing numbers of broad
families of non-adequate prime satellite knots. More specifically, we exhibit
minimal crossing number diagrams for untwisted Whitehead doubles of zero-writhe
adequate knots. This allows us to determine the crossing number of untwisted
Whitehead doubles of any amphicheiral adequate knot, including, for instance,
the Whitehead doubles of the connected sum of any alternating knot with its
mirror image.
  We also determine the crossing number of the connected sum of any adequate
knot with an untwisted Whitehead double of a zero-writhe adequate knot.
