1. How this works… Algebra 2 HSAPers
Each correct answer wins you 1 “ticket”.
“Prizes” you can trade your “tickets” in for:
10 tickets = 1 extra point on a test/project (from Q4)
30 tickets = 100 homework grade
40 tickets = 100 quiz grade
If you get all 106 correct it will count as if you got 110 correct.

2. How this works… Algebra 2 Non-HSAPers
Each correct answer wins you 2 “tickets”.
“Prizes” you can trade your “tickets” in for:
10 tickets = 1 extra point on a test/project (from Q4)
30 tickets = 100 homework grade
40 tickets = 100 quiz grade
If you get all 54 correct it will count as if you got 55 correct.

3. Please work out this problem in your notes…
Graph the following function and sketch the graph: −2 𝑥 3 − 𝑥 2 +5𝑥+6

4. Check Packets from HSAP week

5. Polynomial Functions and Their Graphs
Section 7.2
Polynomial Functions and Their Graphs

6. Does this graph have a max? min?
Why? Can infinity or negative infinity be a max or min?
Local maximum: a relative maximum; where the graph makes a U-turn increasing to decreasing
Plural is local maxima
Local minimum: a relative minimum; where the graph makes a U-turn decreasing to increasing
Plural is local minima

7. Increasing vs. Decreasing
When we look at where a function is increasing or decreasing we always read left to right.
Which does this function do first?
Where else is it decreasing?
Where is it increasing?

8. Notation
How do we know exactly where the function changes from increasing to decreasing?
Use our calc to find local max and min.
Notation: local max. ( , ) local min. ( , )
Increasing: ( , ) & ( , )  in terms of x
Decreasing: ( , ) & ( , )  in terms of x

9. Practice:
Graph each of the following functions. Find any local maxima or minima to the nearest tenth. Find the intervals over which the function is increasing and decreasing. 𝑃 𝑥 =−3 𝑥 3 +5 𝑥 2 +𝑥+2 𝑃 𝑥 = 𝑥 4 −2 𝑥 2 +2

10. 𝑃 𝑥 =−3 𝑥 3 +5 𝑥 2 +𝑥+2
Local Maximum: (1.2, 5.2) Local Minimum: (-0.1, 2.0) Increasing: (-0.1, 1.2) Decreasing: (-, -0.1) & (1.2, )

11. 𝑃 𝑥 = 𝑥 4 −2 𝑥 2 +2
Local Maximum: (0, 2) Local Minima: (-1.7, 1) , (0.3, 1) Increasing: (-1.7, 0) & (0.3, ) Decreasing: (-, -1.7) & (0, 0.3)

12. Homework: Worksheet 7.2
5 – 12 ONLY

13. Products and Factors of Polynomials
Section 7.3
Products and Factors of Polynomials

14. Factoring the Sum and Difference of Two Cubes
𝑎 3 + 𝑏 3 =(𝑎+𝑏)( 𝑎 2 −𝑎𝑏+ 𝑏 2 ) 𝑎 3 − 𝑏 3 =(𝑎−𝑏)( 𝑎 2 +𝑎𝑏+ 𝑏 2 )

15. Factor Theorem
(x-r) is a factor of the polynomial expression that defines the function P if and only if r is a solution of P(x) = 0, that is, if and only if P(r) = 0.
In other words:
Set x-r = 0
Solve for x. x = r
Plug this r in for every x in the original polynomial
Simplify
If you get 0 then (x – r) IS a factor of the polynomial