Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
9-3 5/24/2017 9-3 Finding Polynomial Models 9-3 5/24/2017 Determining Degree Give me an equation of a line where the slope is a whole number: f(x) = Give me a quadratic equation with whole numbers for A, B, & C: f(x) = Give me a 3rd degree polynomial with whole number coefficients: f(x) = x 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 f(x) Diff: x f(x) Diff: 2nd diff: x f(x) Diff: 2nd diff: 3rd diff: 9-3 5/24/2017 Determining Degree If you know a list of numbers comes from a polynomial model, you can determine the degree of the polynomial by: • Find the difference between consecutive terms • If the differences are the same, it is a linear function (degree 1) • If not, find the difference of the differences. • Repeat until the differences are constant. • The number of times you have to find the difference is the degree of the polynomial. 9-3 5/24/2017 Determining Degree x 1 2 3 4 5 6 f(x) -14 2 36 130 350 786 Diff 2nd Diff 3rd Diff 4th Diff The 4th Differences are constant so these came from a 4th degree polynomial 9-3 5/24/2017 Finding a Model To find a polynomial model: x 1 2 3 4 f(x) 7 4 5 16 • Find the degree • Enter data into lists in the Calculator. • To appropriate regression to get model. This is degree 3 a = 1 b = -4 c = 2 d = 8 f(x) = x3 – 4x2 + 2x + 8 9-3 5/24/2017 Application Jeff thinks it would be fun to roll a marble down a hill and record the distance away from him the marble goes after each second. He records the following information: After 1 second, the marble was 1 inch away, after 2 seconds, it was 4 inches away, after 3 seconds, it was 10 inches away, after 4 seconds, it was 20 inches, and after 5 seconds, it was 35 inches away. Something caught Jeff’s attention after 5 seconds, and he was not able to see how far away the marble was after 6 seconds. Find a model for this data so you can help him figure it out. 9-3 5/24/2017 Things to be careful of: The independent values in the table MUST represent an arithmetic sequence. Remember, we are looking for a CONSTANT difference. The direction you take to find your differences must remain consistent throughout the “row” of differences. You can only change direction with a new row of differences, not in the middle of the row to keep the math “easier”.