do now 3/6/2012

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Do Now 3/6/2012 Evaluate f(2) and f(-2): f(x) = x 3 – x 2 – 4x + 4

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Do Now 3/6/2012. Evaluate f(2) and f(-2): f(x) = x 3 – x 2 – 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 - PowerPoint PPT Presentation

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Page 1: Do Now 3/6/2012

Do Now 3/6/2012 Evaluate f(2) and f(-2):

f(x) = x3 – x2 – 4x + 4

Page 2: Do Now 3/6/2012

Today’s Objective: Graph polynomial functions and locate

real zeros

Find the relative maxima and minima of polynomial functions

Page 3: Do Now 3/6/2012

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

Page 4: Do Now 3/6/2012

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

Page 5: Do Now 3/6/2012

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

Page 6: Do Now 3/6/2012

Graph coordinates Connect points with smooth curves Remember this is a sketch it does not have

to be perfect

Page 7: Do Now 3/6/2012

Graph a Polynomial Function

Graph f(x) = –x3 – 4x2 + 5 by making a table of values.

Answer:

Page 8: Do Now 3/6/2012

Do Now What is a relative minimum and

maximum?

Page 9: Do Now 3/6/2012

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.

Page 10: Do Now 3/6/2012

Analyzing Polynomial functions Create a table of values

Identify number of zeros Identify relative maximum

and minimum points

Explain turning points and make predictions

Page 11: Do Now 3/6/2012

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.