You can put this solution on YOUR website! How many times does the parabola
y=4x^2-12x+9 intersect the x-axis?
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Check the determinant.
b^2-4ac = 12^2-4*4*9 = 0
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The parabola touches the x-axis at x = -b/2a = 1.5
but does not pass thru it.
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Cheers,
Stan H.