Can Bi-Quadratic Equations Be Represented in 3-Dimensional Graphs?

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Discussion Overview

The discussion revolves around the representation of bi-quadratic equations in three-dimensional graphs, specifically exploring the possibility of overlapping graphs and methods for visualizing the equations in two-dimensional axes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants inquire whether a bi-quadratic equation can be graphed in three dimensions, noting that Z represents a surface in three-dimensional space as a function of X and Y.
  • There is a suggestion to break the equation into two parts for two-dimensional graphing or to overlap the two parts on a single graph.
  • One participant proposes creating a contour plot in the XY plane or taking a slice along another plane by setting X or Y to a constant to obtain a 2D graph.

Areas of Agreement / Disagreement

Participants express varying approaches to visualizing the bi-quadratic equation, with no consensus on a single method or solution for overlapping graphs or dividing the equation.

Contextual Notes

Participants do not specify the exact nature of the bi-quadratic equation or the parameters involved, leading to potential ambiguity in the discussion.

Windseaker
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Trying to solve a bi-quadratic eq. so I can graph in in x and y , but Z means this is a 3-D graph? , is it possible to have a overlapping graph or any ideas?? X= +100 &-100

Z= a + bX + cX² + dY + eY² + fXY
 
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Windseaker said:
Trying to solve a bi-quadratic eq. so I can graph in in x and y , but Z means this is a 3-D graph? , is it possible to have a overlapping graph or any ideas?? X= +100 &-100

Z= a + bX + cX² + dY + eY² + fXY

The equation Z= represents a surface in 3 space, as a function of X and Y. What are you trying to solve?
 
Im trying to break the equation into two parts to graph on a two dimensional axis or overlap the two on one graph, any ideas on dividing the equation into two??
 
Windseaker said:
Im trying to break the equation into two parts to graph on a two dimensional axis or overlap the two on one graph, any ideas on dividing the equation into two??

It depends what you what to show. You could make a contour plot in the xy plane. Or take a slice along some other plane. Just set x or y to a constant and it becomes a 2D graph.
 
too easy, thank you
 

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