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How to sketch in 3d watch

1. Hello if you have something like y = x^2 + 2

you can just go through some values of x and obtain y and get a rough sketch.

Or in 2d you usually know what the function looks like like y = x^2 is a paraboloa so y=x^2 + 2 is a parabola where y = 2 when x =0

How do you do this in 3d any tips I mean i'm trying to sketch

y = 2x^2 + 2z^2

any tips for sketching 3d graphs

thanks
2. (Original post by SFquestion)
Hello if you have something like y = x^2 + 2

you can just go through some values of x and obtain y and get a rough sketch.

Or in 2d you usually know what the function looks like like y = x^2 is a paraboloa so y=x^2 + 2 is a parabola where y = 2 when x =0

How do you do this in 3d any tips I mean i'm trying to sketch

y = 2x^2 + 2z^2

any tips for sketching 3d graphs

thanks
You could try taking slices.

If x=0, then y=2z^2, a parabola in the x=0 plane.
x=1, then y= 2 + 2z^2, again a parabolw shifted by 2 in the x=1 plane
x=2,...

Similary fix z=0, etc, to get the shape in the z=0 plane.

Also notice y = 2 (x^2+z^2). The part in brackets is the formula for a circle with radius root(y/2)

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