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

Assuming f(x) = (x+6)^2 + 3

g(x) = -2(x+6)^2 +2

Vertex (-6, 2)

A "horizontal shrink" by a factor of 1/2 means that the graph actually got narrower. Although it is called a "horizontal shrink." you can think of it as, in the horizontal direction, the graph shrunk by a a factor of one half, or it got twice as narrow with respect to the y-axis being the vertical line of symmetry. This implies the graph actually had a vertical stretch of 2. The nomenclature makes this topic more difficult than it needs to be.