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.

steps below

Step-by-step explanation:

f(x)=(x+6)²+3  ... Gray graph

horizontal shrink by a factor of 1/2: f(2x) = (2x+6)²+3 ... green

translation 1 unit down: f(2x)-1 = (2x+6)²+2   ... purple

reflection in the x-axis: g(x) = - ((2x+6)²+2) = - (2x+6)²-2 = -4(x+3) - 2  .. Red

parabola equation: y = a(x-h)² + k    (h,k): vertex

vertex (-3 , -2)

the answer is 0.071

good luck! : d