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

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SUMMARY

The discussion centers on representing bi-quadratic equations in three-dimensional graphs, specifically the equation Z = a + bX + cX² + dY + eY² + fXY. Participants confirm that this equation defines a surface in three-dimensional space as a function of X and Y. To visualize this equation, users can create contour plots in the XY plane or take slices by setting either X or Y to a constant, effectively transforming the 3D graph into a 2D representation.

PREREQUISITES
  • Understanding of bi-quadratic equations
  • Familiarity with 3D graphing concepts
  • Knowledge of contour plots
  • Basic skills in manipulating mathematical equations
NEXT STEPS
  • Learn how to create contour plots using tools like MATLAB or Python's Matplotlib
  • Explore 3D graphing techniques in software such as GeoGebra or Desmos
  • Study the concept of slicing in 3D graphs to visualize equations
  • Investigate the application of bi-quadratic equations in real-world scenarios
USEFUL FOR

Mathematicians, educators, students in advanced mathematics, and anyone interested in visualizing complex equations in three-dimensional space.

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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