Quadratic functions and graphs

problem
Fence it

Age

11 to 14

Challenge level

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
problem
What's that graph?

Age

14 to 18

Challenge level

Can you work out which processes are represented by the graphs?
problem
Guessing the graph

Age

14 to 16

Challenge level

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
problem
Which quadratic?

Age

14 to 18

Challenge level

This task develops knowledge of transformation of graphs. By framing and asking questions a member of the team has to find out which mathematical function they have chosen.
problem
Geometric parabola

Age

14 to 16

Challenge level

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
problem
Minus one two three

Age

14 to 16

Challenge level

Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?
problem
'Tis whole

Age

14 to 18

Challenge level

Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?
problem
Integral inequality

Age

16 to 18

Challenge level

An inequality involving integrals of squares of functions.
problem
Parabolas again

Age

14 to 18

Challenge level

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

Age

16 to 18

Challenge level

This is a beautiful result involving a parabola and parallels.