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.