Exploring Polynomial Functions

Look at the "Polynomial form f(x)" line on the right screen. a. What is the degree of f(x)? Is it odd or even? b. Describe the direction of each end of the graph. (Point up or down?) c. Now change a to a negative number. Describe the direction of each end of the graph. Scroll down to do more questions.

Now slide either n, k or s to get the odd degree. Change a = 1. a. What is the degree of f(x)? b. Describe the direction of each end of the graph. (Point up or down?) Now slide a from positive to negative. c. Describe the direction of each end of the graph. (Point up or down?)

Use the answer from Question 1, 2 and 3ab, write a summary about the relationship between the degree and the end behavior of the graph of a polynomial function. a. If degree is even and a > 0, then ________. b. If degree is even and a < 0, then _________. c. If degree is odd and a > 0, then _____. d If degree is odd and a < 0, then ________.

Find all x-intercepts on the graph.

a. Compare the x-intercepts on the graph and the factor of f(x) on the right screen. How do you find the x-intercept from a given function like f(x)? b. Compare the y-intercepts on the graph and f(x) on the right screen. Which form would you use to find y-intercept? The factor form or the polynomial form?

Change a = 1, b = -1, c = 1, d = 2, n = 3, k = 2 and s = 1. a. At x = -1, does f cross or touch the x-axis? What is the power of (x+1)? b. At x = 1, does f cross or touch the x-axis? What is the power of (x-1)? c. At x = 2, does f cross or touch the x-axis? What is the power of (x-2)? d. Change n, k and s. Observe when f crosses the x-axis and when f touches the x-axis.