Describe and explain the change in the shape of the graph y=x^2 and y=x^2 + 2.

The graph is translated by two in the positive y-axis direction. For example, for the equation y=x², taking the x-axis values of 0,1,2 and 3, y= 0²,1², 2² and 3²respectively: These values being 0,1,4,9. This forms the parabola, or the 'smiling' shape that we see in the graph. However, when the equation of the graph becomes y=x²+2, the value of y increases by 2 each time. When x=0, y=0+2. When x=1, y=1+2. When x=2, y=4+2, and so on. In this way, it is the y value that increases by a positive unit of 2, rather than the x value.