SOLUTION: 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 = 3x2

Rules for :

If a is positive the parabola opens upward.
If a is negative the parabola opens downward.

Calculate d, the discriminant where the
discriminant is given by 

If d is positive the parabola has exactly 2 points
in common with the x-axis.
If d is negative the parabola has NO points in
common with the x-axis.
Id d is zero the parabola has exactly 1 point in
common with the x-axis, and that one point is the 
vertex of the parabola.

Then calculate a*d
If a*d is positive, the vertex is below the x-axis
If a*d is negative, the vertex is above the x-axis 
If a*d is zero, the vertex is on the x-axis

In your problem a=3, b=-12, c=12, so

Since a=3 is positive the parabola opens upward.

We calculate d:


So the discriminant is 0, and ad = 0, so the vertex
is on the x-axis and has only that one point in
common with the x-axis.

Now that we have done it without the graph, we can
check by drawing the graph:



Edwin