Writing in Math Use the information about foreign­born population, algebra homework help

Writing in Math Use the information about foreign ­born population on page 359 to explain how graphs of polynomial functions can be used to show trends in data. Include a description of the types of data that are best modeled by polynomial functions and an explanation of how you would determine when the percent of foreign­born citizens was at its highest and when the percent was at its lowest since 1990.

6-5
Analyzing Graphs of
Polynomial Functions
Main Ideas
. Graph polynomial
functions and locate
their real zeros.
. Find the relative
maxima and minima
of polynomial
functions
GET READY for the Lesson
The percent of the United
Foreign-Born Population
States population that was
foreign-born since 1900
can be modeled by P(t) =
0.000064 -0.007+ +0.05+ +
14, where t = 0 in 1900. Notice
that the graph is decreasing
from t = 5 to t = 75 and then
it begins to increase. The
points at t = 5 and 1 = 75 are
turning points in the graph.
20 40 60 80+
Years Since 1900
Percent of U.S.
Population
POI
18
16
14
12
10
8
6
4
2
TNT
New Vocabulary
Location Principle
relative maximum
relative minimum
0
Graph Polynomial Functions To graph a polynomial function, make a
table of values to find several points and then connect them to make a
smooth continuous curve. Knowing the end behavior of the graph will
assist you in completing the sketch of the graph.
Study Tip
EXAMPLE
Graph a Polynomial Function
Graph flx) = x + x – 4×2 – 4x by making a table of values.
f)
f
(36)
Graphing
Polynomial
Functions
-2.5
= 8.4
0.0
0.0
-2.0
0.0
0.5
-2.8
-1.5
28-13
1.0
-6.0
To graph polynomial
functions it will often
be necessary to include
x-values that are not
integers.
-1.0
0.0
15
-6.6
05
= 0.9
2.0
0.0
f(x) = x + x – 4×2 – 4x
This is an even-degree polynomial with a positive leading
coefficient, so f(x) + + asx + + , and fx) + + asx – 0.
Notice that the graph intersects the x-axis at four points, indicating
there are four real zeros of this function.