y=x²+x-6 (original form ax²+bx+c)
1) this is a parabola open upward since the coefficient of x² is positive
so it has a minimum.
2) Its symmetry line = -b/2a = -1/2 & for x=-1/2, y= 23/4
So its minimum is (-1/2, 23/4)
3) Now to see if the parabole intercepts the x-axis we calculate the roots of
x²+x-6. As you will notice Δ <0 so there is no roots & consequently it doesn't intersect with x-axis
Your graph is wrong, and the parabola should be above the x-axis & it will intersect with the y-axis at y=23/4 =5.75nunits