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)

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;