document.write( "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?
\n" ); document.write( " A. 1955, 47.6 years old
\n" ); document.write( "B. 1936, 47.6 years old
\n" ); document.write( "C. 1955, 24.9 years old
\n" ); document.write( "D. 1951, 36 years old
\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #304128 by ewatrrr(24785) $\"\"$ $\"About$

You can put this solution on YOUR website!

 
\n" );
document.write( "Hi, Note use of ^ (uppercase 6)
\n" );
document.write( "Using the vertex form of a parabola,  where(h,k) is the vertex
\n" );
document.write( "f(x) = 0.0037x^2 – 0.41x +36.23  |graphically a parabola opening upward a>0
\n" );
document.write( "models the average age at which Kentucky men were first married x years 'after 1900'
\n" );
document.write( "f(x) = 0.0037x^2 – 0.41x +36.23  |Completing square to find the vertex (min point)
\n" );
document.write( "f(x) = .0037[(x - 55.4)^2 - 3069.7589] + 36.23
\n" );
document.write( "f(x) = .0037(x - 55.4)^2 - 11.36 + 36.23
\n" );
document.write( "f(x) = .0037(x - )^2 + 
\n" );
document.write( "The year, average age at a minimum: 1900+55 = 1955  
\n" );
document.write( "The average age at first marriage: 24.9\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "  \n" );
document.write( "

\n" );