The following graph of f(x) = x2 has been shifted into the form f(x) = (x − h)2 + k: a parabola with a vertex of 2, 3 what is the value of k?

We are given

and it has been shifted to get form

where

vertex is (h,k)

and we are given vertex as (2,3)

now, we can compare

and then we can solve for k

and we get

..............Answer

The value of is in the equation of the parabola with the vertex at .

The given function of the curve is which is being shifted to   with the vertex at .

According to the question, is the vertex of the parabola.

So, compare the parametrs,

Hence, the value of is in the equation of the parabola with the vertex at .

Learn more about parabola here:

link

a

step-by-step explanation:

the answer is a

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;