do now 3/6/2012
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Do Now 3/6/2012 Evaluate f(2) and f(-2):
f(x) = x3 – x2 – 4x + 4
Today’s Objective: Graph polynomial functions and locate
real zeros
Find the relative maxima and minima of polynomial functions
Vocabulary Location Principle-
if f(a)< 0 and f(b) > 0, then there exists at least one zero between a and b
Relative maximum- a point on the graph of a function where no other nearby points have a greater y-coordinate
Relative minimum- a point on the graph of a function where no other nearby points have a lesser y-coordinate
Analyzing Graphs of polynomial functions
Graphing polynomial functions Identify the end behavior Create a table of values Graph and connect points through smooth
curves Analyzing
Locate zeros of a Function Identify maximum and minimum points Explain turning points and make predictions
Graphing polynomial functions
Create a table of values f(x) = x3 – 5x2 + 3x + 2
Identify maximum number of zeros possible Plug in x values to find f(x) Extend table until you reach the
maximum change in signs
Graph coordinates Connect points with smooth curves Remember this is a sketch it does not have
to be perfect
Graph a Polynomial Function
Graph f(x) = –x3 – 4x2 + 5 by making a table of values.
Answer:
Do Now What is a relative minimum and
maximum?
Relative Minima and Maxima In order to find:
Create an xy-table Look at y values for increase and decrease
in 3 consecutive values If values increase and decrease between 3
consecutive numbers then there exist a relative maximum
If values decrease then increase there exist a relative minimum.
Analyzing Polynomial functions Create a table of values
Identify number of zeros Identify relative maximum
and minimum points
Explain turning points and make predictions
Maximum and Minimum Points
Graph f(x) = x3 – 4x2 + 5. Estimate the x-coordinates at which the relative maxima and minima occur.
Make a table of values and graph the function.
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