Exercise 3 Page 145

A quadratic function of the form f(x) = a(x-h)^2 is a transformation of the simpler function q(x)=ax^2, which has its vertex at the origin. To see the effects of the parameter h we can graph some example functions of each form together, changing the values of h and keeping a constant.

In the graph above we can see three different functions with a=1. Note that when h=2, the graph is shifted 2 units to the right. On the other hand, when h=- 2 the graph is shifted 2 to the left instead. By considering these observations and the effects of a, we can describe any graph of the form f(x) = a(x-h)^2.

• If a<0 the graph is reflected in the x-axis.
• If 0 < |a| <1 the graph is vertical shrunk.
• If 1 < |a| the graph is vertical stretched.
• If h>0 the graphs is horizontally translated h units to the right.
• If h<0 the graphs is horizontally translated |h| units to the left.