Exercise 4 Page 419

We are given the graph shown below.

Since the graph is of the form y=ax^2, we can compare the graph to that of the simplest case, y=x^2. This will allow us to see how it is being affected by the parameter a.

As we can see, the graph given has the y-values decreased in comparison with y=x^2, taking the graph closer to the x-axis. It is a vertical shrink of y=x^2. Let's review the effects that the parameter a has on a function of the form y=ax^2, according to its value.

• If a<0 it causes a reflection in the x-axis.
• If 0 < |a| <1 it causes a vertical shrink, taking the graph closer to the x-axis.
• If 1 < |a| it causes a vertical stretch, taking the graph away from the x-axis.

Since our graph is not reflected in the x-axis and presents a vertical shrink, the possible values for the parameter are 0