Find the amount of direction of shift in the curve between y=x² and y=(x-2)² ?
This question can be solved using the concept of shifting of graphs. This is a highly important concept not just for functions but also for co-ordinate geometry, one you will utilise numerous times while solving questions from these topics. 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.