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

y=-2x^2+x-3

y=-2x^2+x-3=-2(x^2-1/2 x)-3=-2(x-1/4)^2+2*1/16-3=-2(x-1/4)^2+1/8-3=-2(x-1/4)^2-2 7/8

y=-2(x-1/4)^2-2 7/8<=-2 7/8

So there is no points the parabola has in common with the x-axis.

Its vertex lies below the x-axis.

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