Find the turning point of the curve whose equation is y = (x-3)^2 + 6.

The turning point can be found by using the concept of transformations. Firstly, it is important to form a relation between the values of a and b in an equation of the following form y = (x+a)^2 + b and the turning point of such an equation. Using the understanding of this relationship it becomes easy to deduce the turning point of any curve in this form.
Plotting a curve of y = x^2 shows the turning point to be (0,0). Next, plot the curve of y = (x+1)^2 by inputting values of x to find the corresponding y values. Try this again with y = (x+1)^2 + 1. Note the turning points for all these curves with different values for a and b. While experimenting with values for a and b, it should eventually become clear that for a curve of y = (x+a)^2 + b the turning point lies at (-a,b) and therefore for this equation the turning point is (3,-6).