Find the amount of direction of shift in the curve between y=x² and y=(x-2)² ?

JEE Shifting of Graphs

This question can be solved using the concept of shifting graphs. This is a highly important concept not just for functions but also for coordinate geometry, one you will utilise numerous times while solving questions from these topics.

Understanding The Concept And Finding Solution

The concept is simple : For a positive constant c, the graph of function y=f(x+c) is shifts c units in the negative x direction by a magnitude of c.

Now coming back to our question, the value of c= -2. So, the graph will shift 2 units in the positive x direction. It simply means that the values of y that occurred initially at x, will now occur at (x+2).

This can be easily verified as follows: For the original function, y= 0 occurs at x=0 that is, at the origin. Let us check what happens in the case of new function y=(x-2)² .

Putting y=0, we get 0=(x-2)²

Taking the square roots,  x-2 = 0 => x=2

This implies that y=0 now occurs at x=2 that is, it has shifted 2 units in the positive x direction. The same can be concluded for all values of y and therefore, the entire graph shifts.