![Parabolic Patterns](/sites/default/files/styles/medium/public/thumbnails/content-01-04-six6-icon.jpg?itok=ooCB4f1a)
problem
Parabolic Patterns
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.
![Doesn't add up](/sites/default/files/styles/medium/public/thumbnails/content-97-03-six3-icon.jpg?itok=nUZvwIt5)
problem
Doesn't add up
In this problem we are faced with an apparently easy area problem,
but it has gone horribly wrong! What happened?
![Exploring cubic functions](/sites/default/files/styles/medium/public/thumbnails/content-01-10-six5-icon.png?itok=ZWMuoWlI)
problem
Exploring cubic functions
Quadratic graphs are very familiar, but what patterns can you explore with cubics?
![Perpendicular lines](/sites/default/files/styles/medium/public/thumbnails/content-id-5610-icon.jpg?itok=1D6L2o09)
problem
Perpendicular lines
Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?
![Negatively Triangular](/sites/default/files/styles/medium/public/thumbnails/content-id-5871-icon.jpg?itok=rb_qXMmk)
problem
Negatively Triangular
How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
![At right angles](/sites/default/files/styles/medium/public/thumbnails/content-id-6461-icon.jpg?itok=G0r90Rd3)
problem
At right angles
Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
![Back fitter](/sites/default/files/styles/medium/public/thumbnails/content-id-6506-icon.gif?itok=gbCv-A6B)
problem
Back fitter
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
![Surprising Transformations](/sites/default/files/styles/medium/public/thumbnails/content-id-6544-icon.jpg?itok=48Xkr569)
problem
Surprising Transformations
I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?
![What's that graph?](/sites/default/files/styles/medium/public/thumbnails/content-id-7502-icon.jpg?itok=LHizmXXB)
![Tangled Trig Graphs](/sites/default/files/styles/medium/public/thumbnails/content-id-6481-icon.jpg?itok=RNf074BX)
problem
Tangled Trig Graphs
Can you work out the equations of the trig graphs I used to make my pattern?
Image
![Functions & Graphs - Stage 4 STEM footer Functions & Graphs - Stage 4 STEM footer](/sites/default/files/styles/large/public/thumbnails/content-id-13489-STEMlogo.png?itok=3GoGVsIW)
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.