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

In summary, the conversation discusses the possibility of graphing a bi-quadratic equation in x and y, but the inclusion of Z makes it a 3-D graph. The speaker is looking for ideas on how to divide the equation into two parts to graph it in a 2-D axis or overlap them on one graph. They mention the option of creating a contour plot or taking a slice along a different plane to simplify the graph.
  • #1
Windseaker
46
0
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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  • #2
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?
 
  • #3
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??
 
  • #4
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.
 
  • #5
too easy, thank you
 

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

1. What is a bi-quadratic curve or curve?

A bi-quadratic curve, also known as a biquadratic curve, is a type of curve that is represented by a polynomial equation of degree four. It is a two-dimensional curve that can be graphed on a coordinate plane.

2. How is a bi-quadratic curve different from a quadratic curve?

A bi-quadratic curve is different from a quadratic curve in that it has a higher degree of four, while a quadratic curve has a degree of two. This means that a bi-quadratic curve can have up to four x-intercepts, while a quadratic curve can only have two.

3. What are the key features of a bi-quadratic curve?

The key features of a bi-quadratic curve include its degree of four, its symmetry about the y-axis, and its possible four x-intercepts. It can also have a maximum or minimum point, depending on the coefficients of the equation.

4. How is a bi-quadratic curve used in real life?

Bi-quadratic curves are used in various fields of science, such as physics, engineering, and economics, to model and analyze different types of data. They can be used to represent the relationship between two variables, such as time and distance, and make predictions or solve problems.

5. What are some common examples of bi-quadratic curves?

Some common examples of bi-quadratic curves include parabolas, hyperbolas, and ellipses. These curves can be represented by a bi-quadratic equation, and their shapes and properties can be studied and applied in different fields of science and mathematics.

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