Try sketching the graph of y=x2 on paper. What would you expect the graph
of y=-x2 to look like? What is the effect
of the minus sign? Is this one of the graphs in the picture?
What would you expect the graph of y=(x-4)2 to look like? How would you
expect the graph of y=x2 to be transformed to give the graph of y=(x-4)2?
What about y=-(x-4)2?
Draw the graphs of these functions using graph
drawing software or a graphics calculator if you have access to one
or the other. Were your predictions right?
What have you learnt from this example about reflections and translations of
graphs and the corresponding equations of the functions?
Now experiment with drawing the graphs of other functions and see if you can
find the equations for all the graphs in the picture.