Question

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

  1. \(a=0\),

  2. \(a=\pm1\),

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

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