Notes 3­7 Investigating Graphs of Polynomials Functions
Objectives:
­ Use properties of end behavior to analyze, describe, and graph polynomial functions.
­ Identify and use maxima and minima of polynomial functions to solve problems.
Who uses this?
Welders can use graphs of polynomial functions to optimize the use of construction materials. 1
End behavior is a description of the values of the function as x approaches or negative infinity
positive infinity
The degree and leading coefficient of a polynomial determine its end behavior. 2
3
Ex. Identify the leading coefficient, degree, and end behavior.
a.
b.
4
Try These:
Ex. Identify the leading coefficient, degree, and end behavior.
a.
b.
5
Ex. Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.
a.
b.
6
Try These:
Ex. Identify whether the function graphed has an odd or even degree and positive or negative leading coefficient.
a.
b. 7
8
Ex. Graph the function
9
Try These:
Ex. Graph the function
10
A turning point is where the graph changes from increasing to decreasing or from decreasing to increasing.
11
Ex. Graph
maxima and minima. on a calculator, and estimate the local Step 1: Graph.
Step 2: Find the local maxima
Press 2nd + TRACE. Choose 4:MAXIMUM. Step 3: Find the local minima
Press 2nd + TRACE. Choose 3:MINIMUM
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Ex. A welder plans to construct an open box from an 18.5 ft by 24.5 ft sheet of metal by cutting squares from the corners and folding up the sides. Find the maximum volume of the box and the corresponding dimensions. 13