5.1 Polynomial Functions and Models
Graph of a polynomial function
Power function
Find a polynomial of degree 3 whose zeros are -4, -2, and 3.
f  x   a  x  4 x  2 x  3
For the polynomial, list all zeros and their multiplicities.
f  x   2  x  2  x  1  x  3
3
4
Turning points: Points where the graph
changes from an increasing function to
a decreasing function, or vice versa.
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f  0  6 so the y intercept is  6.
The degree is 4 so the graph can turn at most 3 times.
For large values of x, end behavior is like x 4 (both ends approach )