Some quadratic expressions do not have roots. That is, if
there may be no value of
for which f(x)=0. On the otrher hand, every quadratic has a turning point. This is a simple consequence of the fact that the value ofthat defines the turning point is the solution to
or 2ax+b=0 The x value of the turning point is then
The turning point may be either a maximum or a minimum, depending on the value of
If
the turning point is a minimum.
If
the turning point is a maximum.