# How can I plot a parametric equation with ±?

I want to draw a parametric equation with ± like the figure below: But I don't get the result I want when I run the following code. What can I do to get it?

ParametricPlot[{x, ±x^2}, {x, 0, 1},
Mesh -> 30, PlotPoints -> 50, AxesOrigin -> {0, 0}]

• PlusMinus is for display purposes. It has no builtin meaning. It is not an operator that returns a value. The plot would normally be produced with Plot[{x^2, -x^2}, {x, 0, 1}, Mesh -> 30, AspectRatio -> 2, PlotStyle -> {RGBColor[0.37, 0.51, 0.71]}] but you could use ParametricPlot[{Abs[x], Sign[x] x^2}, {x, -1, 1}, Mesh -> 60, PlotPoints -> 50, AxesOrigin -> {0, 0}] – LouisB Mar 28 at 0:07
• @LouisB Thank you. I just want to know if MMA has similar multivalued functions participating in drawing. – Please Correct GrammarMistakes Mar 28 at 1:24

This formulation might be useful to you.

±b_ := {b, -b}

ParametricPlot[Thread[{x, ±x^2}], {x, 0, 1}, Mesh -> 30,
PlotPoints -> 50, AxesOrigin -> {0, 0}] ### Notes

• This will expand appearances of ±value outside of plotting as well. If you need ± to persist in data this expansion should be restricted. We can write a custom plotting function, say parametricPlot, that performs this and other expansions, then hands off the data to ParametricPlot.

• The form used above results in shared styling between the positive and negative branches. Reference: Plot draws list of curves in same color when not using Evaluate

You can just do

ParametricPlot[{{x, x^2}, {x, -x^2}}, {x, 0, 1}, Mesh -> 30,
PlotPoints -> 50, AxesOrigin -> {0, 0}] 