How to plot a function whose constant parameters have associated uncertainties in Mathematica 8.0?

Question

Let's assume I want to plot the function $f(x)=a + bx+ cx^{2}$, where experimentally known values of parameters $a, b$ and, $c$ are as follows:

$a=1.01 \pm 0.18$

$b=0.92 \pm 0.11$

$c=2.2 \pm 0.2$

In the absence of uncertainties, we should have a thin curve which is trivial to plot. However, the thickness of the curve will increase depending on the amount of uncertainties. Is there any way to plot such a function with the corresponding "confidence bands" in Mathematica 8.0?

Answer 1

This does what I think you're after, fiddle with options as desired:

With[{a = Interval[1.01 + .18 {-1, 1}], 
  b = Interval[.92 + .11 {-1, 1}], c = Interval[2.2 + .2 {-1, 1}]}, 
 Plot[{Min[a + b*x + c*x^2], 1.01 + .92 x + 2.2 x^2, 
   Max[a + b*x + c*x^2]}, {x, -5, 5}, Filling -> {1 -> {3}}, 
  FillingStyle -> Darker, PlotStyle -> {None, Red, None}]]