Exercise 2 Page 123

As we can see from Exploration 1, the general shape of the graph of a function of the form y=ax^2 is the one shown below.

From this graph we can identify the main characteristics of the function. Notice however that if a<0 the graph is reflected across the x-axis. Therefore, we will only list those general characteristics that are not affected by this possibility.

• The graph is U-shaped.
• The graph is symmetric about the y-axis. The part of the graph to the left of the y-axis is the mirror image of the part to the right of it.
• It touches the x-axis at x=0.
• It is a continuous function, as the graph does not have any gaps.
• Its domain is all real numbers.
• The absolute value of the function increases quickly for large values of x, either negative or positive.
• The absolute value of the function decreases quickly for small values of x, either negative or positive.