parabola transformations

Question

The graph of g is a horizontal shrink by a factor of 1/2 and a translation 1 unit down, followed by a reflection in the x-axis of the graph of f(x)=(x+6)^2+3. Write a rule for g. Then identify the vertex.

Answer 1

f(x) = (x+6)^2 +3 has vertex (-6,3)

horizontal shrink is the same as a vertical stretch

so, = 2(x+6)^2 +3

one unit down, subtract 1

g(x) = 2(x+6)^2 +2 vertex changed to (-6,2) down 1