Question 440156
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Hi, Note use of ^ (uppercase 6)
Using the vertex form of a parabola, {{{y=a(x-h)^2 +k}}} 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(55.4)}}})^2 + {{{highlight(24.9)}}}
The year, average age at a minimum: 1900+55 = 1955  
The average age at first marriage: 24.9