How to draw this grapg on paper

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In summary, the conversation discusses the graph of z=3x^2+2y^2+1 and x^2+y^2<=1 on paper. The speaker mentions getting two parabolas and a line when inputting zeros, but the other person is confused by this. The graph of x^2+y^2=1 is a circle and x^2+y^2<=1 is a disk.
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electron2
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z=3x^2+2y^2+1

x^2+y^2 <=1

on paper

when i input zeros
i get 2 parabolas and a line
 
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  • #2
What? HOW do you get that?

First, z= 3x2+ 2y2+ 1 involves three variables, x, y, and z, and so is a three-dimensional graph. It is, simply, a "paraboloid". It may be that your "two parabolas" are when you take x= 0 and then y= 0. If so, that's not a bad way to start. Imagine, with x= 0, that you are drawing the parabola in the yz-plane. Then with y= 0, you are drawing the parabola in the xz-plane. If you draw your x-z axes on the paper and imagine the y-axis coming out of the paper, then your two parabolas are at right angle to each other. Imagine the full graph rotating around the z-axis to meet those two parabolas.

As for getting a line for [itex]x^2+ y^2\le 1[/itex], I can't make heads of tails out of that! you should know that the graph of [itex]x^2+ y^2= 1[/itex] is a circle with center at (0,0) and radius 1. The graph of [itex]x^2+ y^2\le 1[/itex] is all points on or inside that circle- a "disk".
 

1. How do I choose the correct graph paper for my drawing?

The type of graph paper you choose will depend on what type of graph you want to draw. For example, if you are drawing a line graph, you will need to use graph paper with evenly spaced horizontal and vertical lines. If you are drawing a bar graph, you will need graph paper with thicker horizontal lines to accommodate the width of the bars.

2. What tools do I need to draw a graph on paper?

You will need a ruler, a pencil, and an eraser. Depending on the type of graph you are drawing, you may also need a protractor or a compass. It is also helpful to have a sharp pencil for precise lines and an eraser for any mistakes.

3. How do I label the axes of my graph?

The vertical and horizontal axes of your graph should be labeled with the appropriate units of measurement. For example, if you are graphing temperature over time, the vertical axis should be labeled with degrees and the horizontal axis with time units (e.g. minutes, hours, days). Always label each axis and include the units to ensure accuracy.

4. How do I plot my data points on the graph?

To plot your data points, use your ruler to draw a small dot at the corresponding point on the graph paper. Make sure the dot is small and precise. You can also use a different symbol or color for each data point to make your graph easier to read.

5. How do I connect the data points on my graph?

Use your ruler and pencil to draw a straight line connecting all of your data points. If you are drawing a line graph, make sure the line is smooth and continuous. If you are drawing a bar graph, make sure the bars are evenly spaced and have the same width. You can also use a different color or pattern for each bar to make your graph more visually appealing.

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