determine how many points parobola has in common with x axis and whether its vertex lies above on or below the x-axis

y=4x^2-12x+12

1 point in common vertex on x -axis

2 points in common vertex below x axis

2 points in common vertex above x axis

no points

=4(x^2-3x)+12

=4(x-3/2)^2-4*9/4+12

=4(x-3/2)^2+3>0

So no points in common with x axis.

The vertex is above x axis.

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