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Broad Topics > Coordinates and Coordinate Geometry > Parabola

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Parabolas Again

Age 14 to 18 Challenge Level:

Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?

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Parabolic Patterns

Age 14 to 18 Challenge Level:

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

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Lattice Points

Age 16 to 18 Challenge Level:

Why are there only a few lattice points on a hyperbola and infinitely many on a parabola?

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Conic Sections

Age 16 to 18

The interplay between the two and three dimensional Euclidean geometry of conic sections is explored in this article. Suitable for students from 16+, teachers and parents.

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More Parabolic Patterns

Age 14 to 18 Challenge Level:

The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.