Age 14 to 18 Challenge Level:
Try sketching the graph of $y=x^2$ on paper. What would you expect
the graph of $y=-x^2$ 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 $y=x^2$ 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
Now experiment with drawing the graphs of other functions and see
if you can find the equations for all the graphs in the picture.