You may also like

problem icon

Quartics

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

problem icon

Sine Problem

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.

problem icon

Folium of Descartes

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

Cocked Hat

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

The implicit equation

$$(x^2 + 2a y -a^2)^2 = y^2(a^2 - x^2)$$

represents a family of functions the members of the family corresponding to different values of $a$.

Re-arrange the equation into the form $y= f(x)$ and draw some graphs belonging to the family for different values of $a$. What is the domain of the function $f(x)$?


For investigating these graphs you can download the shareware program Graphmatica for free from here as NRICH is an approved distributor of this program. You can find more information about the program from http://www.graphmatica.com/ .

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Copyright © 1997 - 2012. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.