1 / 6

6.9 Modeling with Polynomial Functions

6.9 Modeling with Polynomial Functions. p. 380. Ex: Write the cubic function whose graph goes through the points (-2,0), (0,2), (1,0), and (3,0).

abdul-peterson
Download Presentation

6.9 Modeling with Polynomial Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 6.9 Modeling with Polynomial Functions p. 380

  2. 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)

  3. Ex: An eqn. for a polynomial function is f(n)=2n3+n2+2n+1. Show that this function has constant 3rd order differences. (you check the 3rd order diffs. because it’s a degree 3 polynomial) • First, write out the first several values; or find f(1), f(2), f(3),…, f(6). • f(1)=6 f(2)=25 f(3)=70 f(4)=153 f(5)=286 f(6)=481 Now subtract #s! (left from right) 1st diffs. 19 45 83 133 195 Now subtract #s! (left from right) 2nd diffs 26 38 50 62 Now subtract #s! (left from right) 3rd diffs. 12 12 12 ** This is called using finite differences.

  4. Ex:The values of a polynomial function for six consecutive whole numbers are given below. Write a polynomial function for f(n).f(1)= -2, f(2)=2, f(3)=12, f(4)=28, f(5)=50, andf(6)=78 • First, find finite differences. (Stop when the same number repeats all the way across!) 4 10 16 22 28 6 6 6 6 The 2nd differences are now a constant # across. This means the function will be a quadratic. (degree 2) So, use f(n)=an2+bn+c. Since you must find a, b, & c, you will need to make 3 eqns. with these 3 variables using the first 3 known values of the function.

  5. Use an2+bn+c=f(n) & f(1)= -2, f(2)=2, f(3)=12 to write 3 equations. a(1)2+b(1)+c= -2 a+b+c= -2 a(2)2+b(2)+c=2 4a+2b+c=2 a(3)2+b(3)+c=12 9a+3b+c=12 ** Look familiar? It should! ** * Use inverse matrices to solve for a, b, &c! * This means the quadratic is f(n)=3n2-5n+0 or f(n)=3n2-5n

  6. Assignment

More Related