1. 5.4 - Analyzing Graphs of Polynomial Functions

2. Example 1:
Graph f(x) = –x3 – 4x2 + 5 by making a table of values.

3. Location Principle:

4. Example 2:
Determine consecutive values of x between which each real zero of the function is located. Then draw the graph. f(x) = x4 – x3 – 4x2 + 1

5. Maximum & Minimum Points
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.

6. Maximum & Minimum Points
Extrema – max. and min. values of a function.
Turning Point – when the graph turns. Another name for relative max. and min.
- The graph of a polynomial function of degree n has at most n – 1 turning points.

7. Find Extrema on Calculator:
Enter equation into y =.
2nd Calc
Choose 3: minimum or 4: maximum.
Curser on left of min/max, enter.
Curser on right of min/max, enter.
Enter.

8. Example 3: Graph f(x) = -2x3 + 4x2 + 5. Find the zeros of the
function and relative extrema.

9. Example 4: Consider the graph of f(x) = x3 + 2x2 + 7. Estimate
where the relative extrema
occur and find the zeros.

10. Example 5: A) Find the domain and range
B) Find the least possible degree