A parabola passes through the point the point (1,2), (2,1), (3,4) and (4,3). Find the equation of the axis of parabola.

Explanation

To find the equation of the axis of the parabola that passes through the points (1, 2), (2, 1), (3, 4), and (4, 3), we can follow these steps:

### Step 1: Identify the Points
The given points are:
- A(1, 2)
- B(2, 1)
- C(3, 4)
- D(4, 3)

### Step 2: Analyze the Points
Notice that points A(1, 2) and B(2, 1) appear to be reflections of each other across the line y = x. Similarly, points C(3, 4) and D(4, 3) also appear to be reflections of each other across the line y = x.

### Step 3: Confirm the Reflection
To confirm that A(1, 2) and B(2, 1) are reflections:
- The x-coordinate of A is 1, and the y-coordinate of B is 1.
- The x-coordinate of B is 2, and the y-coordinate of A is 2.

Thus, A and B are indeed reflections across the line y = x.

For points C(3, 4) and D(4, 3):
- The x-coordinate of C is 3, and the y-coordinate of D is 3.
- The x-coordinate of D is 4, and the y-coordinate of C is 4.

Thus, C and D are also reflections across the line y = x.

### Step 4: Determine the Axis of the Parabola
Since both pairs of points are reflections across the line y = x, we can conclude that the axis of the parabola is the line y = x.

### Conclusion
The equation of the axis of the parabola is:
\[ y = x \]