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The NRICH weekly challenges are aimed at Post-16 students to provide an interesting, shorter challenge to try out each week which will fit around any usual course of study. Each challenge is designed to be simple to get into and to cover an important and intriguing area of mathematics.
How many will you solve?
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.
Can you find the area of the central part of this shape? Can you do it in more than one way?