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'Cocked Hat' printed from https://nrich.maths.org/
Expand the square the left hand side of the expression and
rearrange the expression to give a quadratic equation in $y$. Now
solve the quadratic equation. This will give two solutions (as
quadratic equations generally do) and each will give you the
equation of a branch of the graph. Sketch the graph by considering
where real values of $y$ exist, where the graph crosses the axes
and what symmetries it has. You can use graphing software but it is
much more of a challenge to sketch the graph without.
Don't let this defeat you. It is not nearly as hard as it looks but
you have to do a little algebra. If you wish you can choose a
particular value for $a$, say $a=1$, and investigate one member of
the family of graphs but then you will have to go back and see what
happens for different values of $a$. You can use graphing software
but it is much more of a challenge to sketch the graph
without.