Complete parts $($a$)$ through $($e$)$ below for the function $f(x)=x^3+15x^2+48x.$

$($a$)$ Identify the graph of $f(x).$

$($b$)$ Identify the turning points.

$($c$)$ Estimate the x$-$intercepts.

$($d$)$ Estimate any local extrema.

$($e$)$ Estimate any absolute extrema.