Estimate the roots of x^2-4x+2=0

Note that g (x) = x^2 - 4x + 0 has roots at x=0 and x = 4 ... The graph opens up and has its vertex at (2,-2)

The graph of x^2 - 4x + 2 has similar roots, but both are closer to the axis of symmetry (which is x = 2).

The graph of x^2 - 4x + 4 has the same axis of symmetry (x = 2) as does x^2 - 4x + 2, but has been translated up by 2 units. This quadratic expression h as only one root: x = 2.

Based on this experimentation, we can safely say that the roots of the given x^2-4x+2 are closer to the axis of symmetry (x = 2). Based upon these graphs, one root of x^2-4x+2 is x = 1/2 approx., and the other is 3 1/2 approx.