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How do I plot a function for a paraboloid? Im putting together surfaces to model lipstick. I need the paraboloid for the top part and then I'll be cutting the paraboloid at angle with another surface. But I can't seem to get a handle on how to plot a simple paraboloid function.

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provide some code sample. Relevant examples you may find here – garej Mar 2 at 21:41
    
thank you, sorry im new to mathematica – Jane Mar 2 at 21:48
    
Welcome to Mathematica.SE! Do not forget to 1) Read the faq! 2) When you see good questions and answers, vote them up by clicking the gray triangles. 3) Also, please remember to accept the answer that solves your problem, by clicking the checkmark sign! – garej Mar 2 at 21:52
    
Alright, Thank You! :) – Jane Mar 2 at 22:00
up vote 10 down vote accepted

For fun:

RegionPlot3D[
 z <= -2 x^2 - 2 y^2 && z <= 8 x + y - 20,
 {x, -10, 10}, {y, -10, 10}, {z, -100, 0},
 PlotPoints -> 150, Mesh -> None, 
 PlotStyle -> Directive[Darker@Red, Specularity[1]],
 Axes -> False, Boxed -> False
]

Mathematica graphics

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beautiful!!! is there a tutorial for this you link me to? i didnt want to copy and paste your work – Jane Mar 2 at 21:45
    
You are welcome to use my code as you see fit. To work with it further, I'd suggest starting with the Mathematica docs, maybe the Basic Plotting Tutorial and moving up from there. This site is also an excellent source of solutions and snippets of useful code. – MarcoB Mar 2 at 21:50
    
Thank You so much Marco!! – Jane Mar 2 at 22:00
Manipulate[
 Plot3D[c (s x^2/a + y^2/b), {x, -1, 1}, {y, -1, 1}],

 {{a, 1}, .1, 5},
 {{b, 1}, .1, 5},
 {{c, 1}, .1, 5},

 {{s, 1}, {1 -> "Elliptic", -1 -> "Hyperbolic"}}
 ]

Mathematica graphics

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The general paraboloid is given by $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=\dfrac{z}{c}$. You can generate the plot using Plot3D.

For example, if $f(x,y)=\dfrac{x^2}{4}+9y^2$, you can plot the function with

f[x_, y_] = x^2/4 + 9y^2
Plot3D[f[x, y], {x, -10, 10}, {y, -10, 10}]

You can refer to the documentation for various plotting and styling options.

enter image description here

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