Point E should be on AD, which is an unfixed point. When E slides, it is necessary to keep ∠ BEF = 120, and X is related to Y. ..

Solution: (1) As shown in the attached figure,? △ Abe's external angle ∠ bed = ∠ A+∠ 1 (the external angle is equal to the sum of two non-adjacent internal angles) is ∠ 2+120 = ∠1+.

∴∠ 1 = ∠ 2, so: △ABE∽△DFE? (There are two groups of angles corresponding to equal)

∴ AE: df = ab: de, that is, x: y = 6: (6-x)

Finishing, y = (-1/6) x&; sup2+x

(2) This is a parabola, which is calculated according to the vertex coordinate formula.

When x = 3, the maximum value of y is 1.5.