{

6.9 – Modeling with Polynomial Functions

Algebra 2

{ {Where We’ve Been Solved

Polynomials: Factoring Rational Roots

Theorem Graphing

Where We Are Going What if you know

the result you are looking for but you don’t know

how to get there?

Rest Stop

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…

Working Backwards

 

Working Backwards

 

Working Backwards

 

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)

Ex: Write the cubic function whose graph goes through the points (-2,0), (0,2), (1,0),

and (3,0).

{

6.9 – Modeling with Polynomial Functions

HW: pg. 383 #14, 15, 17, 18