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 theterm setting this equal to zero and solving. We obtain
We always have to complete the square, even when the coefficient ofis not 1.
The line of symmetry is given by solving the equation