Introduction to Turning Points (Reconstructed)
Introduction to Turning Points
In this activity, we will be looking at graphs of polynomial functions. A polynomial is an expression that deals with powers of ‘x’, such as in this example.
A curve is produced when a polynomial of degree two or higher is graphed. This curve may change direction, beginning as a rising curve and progressing to a high point where it changes direction and becomes a downward curve.
On the contrary, the curve may fall to a low point at which it reverses direction and becomes a rising curve. If the degree is high enough, several of these turning points may occur. There can be as many as one less than the degree of the polynomial.
Objectives:
At the end of this activity, you will be able to:·
Read and describe the graph of a polynomial function in terms of increasing and decreasing.
Understand the relationship between degree and turning points.
Determine the number of possible turning points for a given polynomial function of degree n.
Task:
The function that we see on the graph will have a moving point. Using the slider, identify the coordinates of each turning point. Recall that turning points are the points on a graph where it changes from increasing to decreasing (rising to falling) or from decreasing to increasing (falling to rising).
The task is to utilize GeoGebra Graphing Calculator and its tools to find the degree and coordinates of turning points of the following:
Questions for Discussion:
1. What do you notice about the number of turning points of the cubic function(no. 3)? Quartic functions (no. 2)? How about the quintic function (no. 3)? 2. From the given examples, do you think it is possible for the degree of a function to be less than the number of turning points? 3. State the relation of the number of turning points of a function with its degree n.