Question 1049334
This asks for the vertex, in other words.  Why? The curve is a parabola with its minimum as the vertex and because of symmetry at the vertex, tangent on the curve will have slope 0 there.


A bit of Calculus:  {{{dy/dx=2x-2=0}}}
{{{x-1=0}}}
{{{x=1}}}


{{{y=1^2-2*1+3}}}
{{{y=2}}}


P is (1,2).