Draw each point in the plane coordinate system, as shown in the figure below.

Parabola y = a (x- 1) 2+k, a>0.

Parabolic opening is upward, and the axis of symmetry x= 1.

If point A is on a parabola, point A is the vertex of the parabola:

y=0+k=0，k=0

Solution: y = a (x- 1) 2 > =0 holds.

Then the three points on the parabola must be a, c and e.

Because: CE//x axis

So: point C and point E are symmetrical about parabola symmetry axis x= 1.

But in fact, point C (-1, 2) and point E (4, 2) are not symmetrical about the straight line x= 1.

Suppose that point A on the parabola is not true.

Therefore, point A is not on the parabola.