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.
Age 14 to 18 Challenge Level
Try to decide how the graph of $y=x^2$ is transformed to give the
graphs of $y=ax^2$, $y=(x+b)^2$ and $y=x^2+c$ by experimenting with
some small integer values of $a$, $b$ and $c$, both positive and
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embed rich mathematical tasks into everyday classroom practice.