Question 889807
If y=0 then {{{4x^2-12x+12=0}}}
{{{x^2-3x+3=0}}}
zeros are {{{x=(3+- sqrt(9-12))/2}}}
{{{x=(3+- sqrt(-3))/2}}}  NOT a real number.


The parabola does not share any points with the x-axis.  The vertex is a minimum as found that the coefficient on {{{x^2}}}, 4, is positive; and the vertex is above the x-axis.