Polynomial Functions And Quadratic Models Worksheet - Lecture 6, University Of Florida Page 10
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12L6 - 10
ex. Consider the graph of the polynomial
4
3
2
2
f (x) = x
x
4x
+ 4x = x(x
1)(x
4)
We observe the following about the graph of a poly-
nomial of degree n (text, page 70):
A polynomial function of degree n can have at most
n
1 turning points, and a function with n turning
points must have degree n + 1 or higher (to be shown
later using calculus).
The number of x-intercepts is determined by the
zeroes of the function f (x) (each value of x which is
a solution to the equation f (x) = 0).
The end behavior of a polynomial function as
x approaches
and +
is determined by the
n
highest degree term ax
: the corresponding power
n
function x
, and the sign of leading coefficient a.
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