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How to Graph a Paraboloid

A paraboloid is the surface of revolution of a parabola; that is, it is the shape formed when a parabola is revolved around a third axis. The surface of the reflectors in the headlights of cars are paraboloids. Paraboloids can be expressed by the formula z = b(x^2 + y^2) where b is a constant and x and y are variables.

You can use Excel to make a graph of a paraboloid.

Instructions

- 1
  Choose ranges for x and y. For example, you could choose -1 to +1 for each.
- 2
  Choose a constant for b. For example, you could select b = 3.
- 3
  Enter values for x in column A, starting in cell A2. Begin at the low end of the range chosen in step 1, and, in each row, add a small amount. The exact amount does not matter that much, as Excel will interpolate. In the example, enter -1 in cell A2, then enter = A2+.1 in cell A3 and copy this down to cell A22, where it should be equal to 1.
- 4
  Enter values for y in a similar manner in the top row. In the example, enter -1 in cell B1, then =b1+.1 in cell C1, then copy that across to cell V1 where it should be 1.
- 5
  Calculate values for z. In cell A2 enter =3*($A2^2+B$1^2), where 3 is the value chosen in step 2. Copy this to all the rows and columns that have values.
- 6
  Make the graph. Click "Insert", then "Other charts", then "3D surface" and Excel will plot a paraboloid.

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