We'll write the general form of the quadratic:
ax^2 + bx + c = y
The given 3 points belong to the graph of quadratic function. If the graph passes through the given points, that means that the coordinates of the points verify the equation of the quadratic.
The point (1,2) belongs to the graph if and only if
2 = a*1^2 + b*1 + c
a+b+c = 2 (1)
The point B(1,3) belongs to the graph if and only if
3 = a+b+c (2)
We notice from (1) and (2) that 2 = 3, impossible.
The graph of the quadratic cannot pass through the points (1,2) and (1,3), same time.
So, there is no quadratic function to pass through the given points.