The turning point of the parabola \[y=x^2-2ax+1\] is closest to the origin when

\(a=0\),

\(a=\pm1\),

\(a=\pm \frac{1}{\sqrt{2}}\) or \(a=0\),

\(a=\pm \frac{1}{\sqrt{2}}\).

First we need to find the turning point of the parabola. How might we do this?

How can we work out the distance between this point and the origin?