1. 6.9 – Modeling with Polynomial Functions
Algebra 2

2. Rest Stop Where We’ve Been Where We Are Going Solved Polynomials:
Factoring
Rational Roots Theorem
Graphing
What if you know the result you are looking for but you don’t know how to get there?
Rest Stop

3. Suppose you want to buy a used car that costs about $5,000.
You know the end result: how much you want to spend.
But, how much should you save? What interest rate do you need to make this happen?
For Example…

4. Working Backwards

5. Working Backwards

6. Working Backwards

7. Ex: Write the cubic function whose graph goes through the points (-2,0), (0,2), (1,0), and (3,0).
The 3 x-intercepts (-2, 0), (1, 0), and (3, 0) will give you the 3 zeros of the cubic. They will also tell you 3 factors to use f(x) = a(x + 2)(x – 1)(x – 3).
Then use the 4th point as x & f(x) values:
2 = a(0 + 2)(0 – 1)(0 – 3)
Now solve for a: 2 = 6a so, a = 1/3
Answer: f(x) = 1/3(x + 2)(x – 1)(x – 3)

8. 6.9 – Modeling with Polynomial Functions
HW: pg. 383 #14, 15, 17, 18