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Example 11 from Algebra and Trigonometry, 5.2 Power Functions and Polynomial Functions
Drawing Conclusions about a Polynomial Function from the Graph
What can we conclude about the polynomial represented by the graph shown in Figure 12 based on its intercepts and turning points?
Figure
12
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
The end behavior of the graph tells us this is the graph of an even-degree polynomial. See Figure 13.
Figure 13The graph has 2 x-intercepts, suggesting a degree of 2 or greater, and 3 turning points, suggesting a degree of 4 or greater. Based on this, it would be reasonable to conclude that the degree is even and at least 4.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
What can we conclude about the polynomial represented by the graph shown in Figure 14 based on its intercepts and turning points?
Figure
14
How did it go?