determine how the parabola has in common with the x-axis and whether its vertex lies above on or below the x-axis
here we can rewrite your quadratic function as below:
y = 4 (x-3/2)^2 +3
so the vertex is V = (3/2, 3)
that parabola doesn't intersect the x-axis
the discriminant is negative:
discriminant = 36 - 48 = -12
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