SOLUTION: . The function f(x) = 0.0037x^2 – 0.41x +36.23 models the average age at which Kentucky men were first married x years after 1900. In which year was this average age at a minimum?

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Question 440156: . The function f(x) = 0.0037x^2 – 0.41x +36.23 models the average age at which Kentucky men were first married x years after 1900. In which year was this average age at a minimum? What was the average age at first marriage for that year?
A. 1955, 47.6 years old
B. 1936, 47.6 years old
C. 1955, 24.9 years old
D. 1951, 36 years old


Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi, Note use of ^ (uppercase 6)

Using the vertex form of a parabola, y=a%28x-h%29%5E2+%2Bk where(h,k) is the vertex

f(x) = 0.0037x^2 – 0.41x +36.23  |graphically a parabola opening upward a>0

models the average age at which Kentucky men were first married x years 'after 1900'

f(x) = 0.0037x^2 – 0.41x +36.23  |Completing square to find the vertex (min point)

f(x) = .0037[(x - 55.4)^2 - 3069.7589] + 36.23

f(x) = .0037(x - 55.4)^2 - 11.36 + 36.23

f(x) = .0037(x - highlight%2855.4%29)^2 + highlight%2824.9%29

The year, average age at a minimum: 1900+55 = 1955  

The average age at first marriage: 24.9