Calculate the discriminant and use it to determine how many real-number roots the
equation has.

3x^2 - 6x + 3 = 0

three real-number roots

two real-number roots

one real-number root

no real-number roots

without drawing the graph of the equation, 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 = 2x2 + x - 3

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 in common; vertex below x-axis