Axis of Symmetry
So far, you have investigated the effect of
\(p\) and
\(q\) on the
vertex. What do you notice
about the value of
\(p\) and the axis of symmetry from the
Investigation? The value of
\(p\) gives the location, and the equation, of the axis of symmetry. The axis of symmetry is the line where the function is divided in half, with a mirror image on either side. For quadratic
functions given in
vertex form, the equation of the axis of symmetry is the vertical line
\(x = p\).
Equation of the Axis of Symmetry
The equation of the axis of symmetry for quadratic
functions of the form
\(f(x) = a(x - p)^2 + q \) is
\(x = p\), where
\(p\) is the
\(x\)-coordinate of the
vertex.