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

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?

• Try Plot[With[{w = Interval[1.01 + 0.18 {-1, 1}] + x (Interval[0.92 + 0.11 {-1, 1}] + x Interval[2.2 + 0.2 {-1, 1}])}, {Min[w], Max[w]}], {x, -5, 5}] and report back. – J. M.'s technical difficulties May 21 '16 at 7:12

With[{a = Interval[1.01 + .18 {-1, 1}],

• @Benjamin: I don't have 8.0 installed any more - I'm sure Darker was available in 8, but can't test to explain. Glad you worked around that. As for two or more curves - depends on what you want to do with the confidence bands. Might deserve its own question... – ciao May 22 '16 at 21:23