2 Parabolas Intersecting at 2 Know Points.

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In summary, it is not possible to find the equations of 2 parabolas intersecting at 2 known points, as there exist an infinite number of parabolas passing through those points. Even if the requirement for a vertical axis of symmetry is added, there are still an infinite number of possible equations.
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deltapapazulu
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Is it possible to find the equations of 2 parabolas intersecting at 2 known points? For example, (0, 0) and (50, 3.44).
 
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No. You can construct an infinite number of parabolas passing through two given points.

Even if you require that the parabolas have vertical axis of symmetry there exist an infinite number of parabolas passing through (0,0) and (50, 3.44):
Any such parabola can be written in the form y= ax2+ bx+ c. Setting x=0, y= 0 give 0= c so we still have any parabola of the form y= ax2+ bx passing through (0,0). Set x= 50, y= 3.44 gives 3.44= 2500a+ 50b so b= 0.0688- 50a. Any parabola of the form y= ax2+ (0.688- 50a)x with a any real number passses through (0,0) and (50, 3.44).
 
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This thread was also posted in homework help.
 

FAQ: 2 Parabolas Intersecting at 2 Know Points.

What are parabolas?

Parabolas are U-shaped curves that can be formed by graphing quadratic equations. They have a specific shape and are symmetrical about a line called the axis of symmetry.

How can two parabolas intersect at two known points?

To have two parabolas intersect at two known points, the quadratic equations representing the two parabolas must have the same solutions. This means that the two parabolas will intersect at the same x-values, resulting in two distinct points of intersection.

What does it mean when two parabolas intersect at two known points?

When two parabolas intersect at two known points, it means that the two equations have the same solutions, resulting in two distinct points of intersection. This also means that the two parabolas share the same x-values at the points of intersection.

Can two parabolas intersect at more than two points?

Yes, two parabolas can intersect at more than two points. However, for this to happen, the two parabolas must have more than two solutions in common. This means that the two parabolas will have more than two x-values at which they intersect, resulting in multiple points of intersection.

What is the significance of two parabolas intersecting at two known points?

The significance of two parabolas intersecting at two known points depends on the context in which they are being studied. In mathematics, it can help determine the solutions to a system of equations. In physics, it can represent the paths of two objects in motion that intersect at specific points in time. In general, it can provide valuable information about the relationship between two sets of data or equations.

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