Final answer:
The equation of a parabola that has been vertically compressed by a factor of 1/5 and shifted down 6 units in vertex form is y = (1/5)(x - h)^2 - 6, where (h, k) is the vertex and h is the x-coordinate of the vertex.
Step-by-step explanation:
The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. If a parabola is compressed vertically by a factor of 1/5, the coefficient a would be 1/5. Also, if it is shifted down by 6 units, the k in the vertex form would be -6. Therefore, the desired equation of the parabola in vertex form would be y = (1/5)(x - h)^2 - 6, where h is the x-coordinate of the vertex, which is not given in the problem, and thus remains as the variable h.