The y intercept is F(x) when x=0, i.e., F(0), so y intercept is -2.
The x intercept is when F(x)=0=x^2+3x-2. x^2+3x=2; x^2+3x+9/4=2+9/4; (x+3/2)^2=17/4,
Take square root of each side: x+3/2=±√17/2=±2.06155 approx, so x=-1.5±2.06155.
Two x intercepts: 0.56155 and -3.56155. (x=-1.5 which lies halfway between the intercepts is the axis of symmetry.)