Find the focus and directrix of the parabola y = 1/2(x+1)2 + 4.
C A) Focus: (1,41/2); Directrix: y = 31/2
C B) Focus: (-1,41/2); Directrix: y= 31/2
C C) Focus: (1,31/2); Directrix: y = 41/2
CD) Focus: (-1,31/2); Directrix: y = 41/2

Answer is B! Correct on exam!

Step-by-step explanation:

1. Identify the values for a, h, and k: a= 1/2 h= -1 k= 4. (Remember that the sign of h changes!)

2. Determine vertex: (-1,4)

3. Determine x and y for focus: X= -1 (same as vertex) y= K + 1/4(a)

Substitute what we know into that formula: y= 4 + 1/4(1/2)

y= 4 + 1/2 so y= 4 1/2.

4. Determine directrix: y= k - 1/4(a) ]

Substitute in what we know: y= 4 - 1/4(1/2)

y= 4-1/2 so y= 3 1/2

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4

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;