In this assessment, you will be analyzing the flight path of a loon flying over Limerick Lake. The flight path can be modelled by the equation h(x)=4x46x34x2, where h represents the height above water and x represents the horizontal distance from the centre of the lake in metres. Answer the following questions about the flight of the loon.

Determine the roots of the function by factoring.

Classify the order of each of the roots. What happens to the graph at each of these roots?

Identify the degree and name of the function.

Identify the leading coefficient and end behaviours of the graph.

Sketch the graph WITHOUT the use of technology based on questions 1) to 4).

Use your preferred online graphing tool to graph the function. Compare the function to your solution in 5).

State the domain and range with reasonable restrictions for the context of this problem. Explain.

Explain each part of the graph in context with the given question. Discuss:

What do the end behaviours tell you about the flight path?

What are the reasons for the roots in the flight path?

How does the shape of the graph relate to what the loon is doing?