1. Do Now

2. Section 4.1 Graphing Polynomials
Day 3

3. 1.) Evaluate the polynomial for the given value of x.

4. 2.) Evaluate the polynomial for the given value of x.

5. 3.) Evaluate the polynomial for the given value of x.

6. 1.) degree: 4, leading coef.: -2
Describe the end behaviors of a polynomial, given the degree and the leading coefficient.
1.) degree: 4, leading coef.: -2
2.) degree: 7, leading coef.: 4

7. 3.) degree: 6, leading coef.: 1
Describe the end behaviors of a polynomial, given the degree and the leading coefficient.
3.) degree: 6, leading coef.: 1
4.) degree: 5, leading coef.: -6

8. Example Using the table and knowledge of end behavior
Graph f (x ) = −x 3 + x 2 + 3x − 3 x -2 -1 1 2
f(x)

9. Practice Using the table and knowledge of end behavior
Graph f (x ) = x 4 − x 3 − 4x x -2 -1 1 2
f(x)

10. Think-Pair-Share Match each polynomial function with its graph.
1. f (x ) = x 3 − x
2. f (x ) = −x 3 + x
3. f (x ) = −x 4 + 1
4. f (x ) = x 4
5. f (x ) = x 3
6. f (x ) = x 4 − x 2

11. Sketching a Graph Example
Sketch a graph of the polynomial function f having these
characteristics.
• f is increasing when x < 0 and x > 4.
• f is decreasing when 0 < x < 4.
• f (x ) > 0 when −2 < x < 3 and x > 5.
• f (x ) < 0 when x < −2 and 3 < x < 5.
Use the graph to describe the degree and leading coefficient of f .

12. Sketch a graph of the polynomial
function f having these
characteristics:

13. Closing: Exit Ticket: “What do you know about the graph of
f (x ) = 3.5x 4 + 4x 2 − 7x + 2 without actually graphing the function?”

14. Homework
P ,28;36-40 even

15. Do Now: Using the table and knowledge of end behavior
Graph f (x ) = x 3 − x 2 + x – 1. x -2 -1 1 2
f(x)