shown
below has a line of symmetry about the line
A Level Maths Notes: C1 – Lines of Symmetry for Quadratic Curves
Every quadratic curve has a line of symmetry – it is a basic
property of quadratic curves. For example the curveshown
below has a line of symmetry about the line
For a more complicated quadratic, for example,
we
have to complete the square. In this case we get
The line of symmetry is given by looking at the
term
setting this equal to zero and solving. We obtain
We always have to complete the square, even when the coefficient
of
is
not 1.
For example,
The line of symmetry is given by solving the equation