The table shows projections for the female population of a country $($in millions$).$

$\backslash$table$[[$Year$,2020,2045,2055],[$Female Population,$191,250,272]]$

$($a$)$ Find a quadratic function $f(x)=ax+bx+c$ that gives the female population $($in millions$)$ in year $x,$ where $x=0$ corresponds to the year $2000.$

$($b$)$ Estimate the female population in the year $2050$

$($a$)$ The coefficient of $x^2$ in the equation is $a=$

$($Do not round until the final answer. Then round to three decimal places as needed.$)$