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Broad Topics > Information and Communications Technology > Graph plotters

Cubics

Stage: 4 and 5 Challenge Level:

Knowing two of the equations find the equations of the 12 graphs of cubic functions making this pattern.

Parabolas Again

Stage: 4 and 5 Challenge Level:

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

Parabolic Patterns

Stage: 4 and 5 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.

Enclosing Squares

Stage: 3 Challenge Level:

Can you find sets of sloping lines that enclose a square?

Weekly Challenge 43: A Close Match

Stage: 5 Challenge Level:

Can you massage the parameters of these curves to make them match as closely as possible?

Pitchfork

Stage: 5 Challenge Level:

Plot the graph of x^y = y^x in the first quadrant and explain its properties.

Climbing

Stage: 5 Challenge Level:

Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.

Ellipses

Stage: 4 and 5 Challenge Level:

Here is a pattern for you to experiment with using graph drawing software. Find the equations of the graphs in the pattern.

More Parabolic Patterns

Stage: 4 and 5 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.

Quartics

Stage: 5 Challenge Level:

Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.