determine how many points 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 function as below:
y = -2 (x +1/4)^2 +25/8
so the vertex is V= (-1/4, 25/8) so it doesn't lie above the x-axis.
Furthermore, the discriminant is:
1 - 4*(-2)*(-3) = 1- 24 = -23
discriminant = -23.
being the discriminant negative, then we have no real solutions or roots
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