1. MCS 118 Fall 2013
September 16, 2013

2. MCS 118, 9/16/ Slide #2
Announcements
Calculus tutors, Sun. – Thurs. 6:30 -9:30 pm, Olin Be sure to sign in.
Calculus tutors in Pittman (Mon) and Norelius (Tues) from 7:00 – 9:00 pm
Homework due today.
BK Quiz grades:
Top = 48
Median = 43.5
Average = 40.8
Low = less than 30

3. Terminology for polynomials How the leading term affects the graph
MCS 118 9/16/ Slide #3
Today’s schedule
Terminology for polynomials
How the leading term affects the graph
How the degree affects the number of roots
Sketching the graph of a polynomial

4. Terminology Polynomial Terms Coeffiecients Leading term Degree
MCS 118, 9/16/ Slide #4
Terminology
Polynomial
Terms
Coeffiecients
Leading term
Degree
Constant term

5. The leading term of a polynomial determines the long term behavior.
MCS 118, 9/16/ Slide #5
Leading term
The leading term of a polynomial determines the long term behavior.
This behavior depends on whether the degree is odd or even
and whether the coefficient is positive or negative

6. Degree is odd; leading coefficient is positive
MCS 118, 9/16/ Slide #6
Degree is odd; leading coefficient is positive
F(x) = 325(x3-3x2+2x)
G(x) = 3x5-5x3+12x

7. Degree is even; leading coefficient is positive
MCS 118, 9/16/ Slide #7
Degree is even; leading coefficient is positive
P(x) = x+400x2
Q(x) =x4

8. Leading coefficient is negative
MCS 118, 9/16/ Slide #8
Leading coefficient is negative
y =3x-2x3-1
y=-2x2- 5x,

9. The real zeros of a polynomial
MCS 118, 9/16/ Slide #9
The real zeros of a polynomial
What they are and how to find them
The zeros determine where the graph crosses the x-axis.
A polynomial of degree n can have at most n of them.

10. MCS 118, 9/16/ Slide #10
Example 1: y= x2 + 10x + 25

11. MCS 118, 9/16/ Slide #11
Example 2: y= x5 – x3 - 6x

12. Putting it all together: Graph y = x4-4x2
MCS 118, 9/16/ Slide #12
Putting it all together: Graph y = x4-4x2
Use the leading coefficient test
Find the zeros
Plot a few more points
Draw a continuous curve

13. MCS 118, 9/16/ Slide #13
y = x4-4x2

14. Homework due on Thursday
MCS 118, 9/16/ Slide #14
Coming up:
Homework due on Thursday