2/11/2014 Tuesday, 2/11 You Need: Clickers! Fancy Calculators Possibly textbooks On your desk to be checked during bellwork: Pg. 329 #8,21,22,24,26-30,45,48,49 1 2/11/2014 Chapter 5 Test: Either the 17th and 18th (Monday and Tuesday) or th 18 and block day (19th or 20th) Tuesday and Wed/Thur. Questions on homework will be taken at the end of class. 19 5.8 Polynomial Models in the Real World (n+1) Point Principle For any set of n+1 points in the coordinate plane that pass the vertical line test, there is a unique polynomial of degree at most n that fits the points perfectly. (n+1) Point Principle For any set of n+1 points in the coordinate plane that pass the vertical line test, there is a unique polynomial of degree at most n that fits the points perfectly. Meaning: Any two points determine a unique line. Three points that are not on a line determine a unique parabola. Four points that are not on a line or a parabola determine a unique cubic, etc. 2 2/11/2014 Example 1: Example 1: What polynomial function has a graph that passes through the four points (0,-3), (1,-1),(2,5), and (-1,-7)? What polynomial function has a graph that passes through the four points (0,-3), (1,-1),(2,5), and (-1,-7)? By the (n+1) point principle, there is a _________ polynomial that fits the points perfectly. Example 1: Example 1: What polynomial function has a graph that passes through the four points (0,-3), (1,-1),(2,5), and (-1,-7)? What polynomial function has a graph that passes through the four points (0,-3), (1,-1),(2,5), and (-1,-7)? By the (n+1) point principle, there is a __cubic__ polynomial that fits the points perfectly. By the (n+1) point principle, there is a __cubic__ polynomial that fits the points perfectly. Open a Lists and Spreadsheets Document Example 1: What polynomial function has a graph that passes through the four points (0,-3), (1,-1),(2,5), and (-1,-7)? Example 1: What polynomial function has a graph that passes through the four points (0,-3), (1,-1),(2,5), and (-1,-7)? By the (n+1) point principle, there is a __cubic__ polynomial that fits the points perfectly. By the (n+1) point principle, there is a __cubic__ polynomial that fits the points perfectly. Open a Lists and Spreadsheets Document Open a Lists and Spreadsheets Document Remember, you MUST name your lists, even if it is just “x” and “y”. 3 2/11/2014 Example 1: What polynomial function has a graph that passes through the four points (0,-3), (1,-1),(2,5), and (-1,-7)? By the (n+1) point principle, there is a __cubic__ polynomial that fits the points perfectly. Example 1: What polynomial function has a graph that passes through the four points (0,-3), (1,-1),(2,5), and (-1,-7)? By the (n+1) point principle, there is a __cubic__ polynomial that fits the points perfectly. Click “ctrl” and “doc” (to add a page) Add a Data and Statistics Page Click “ctrl” and “doc” (to add a page) Example 1: What polynomial function has a graph that passes through the four points (0,-3), (1,-1),(2,5), and (-1,-7)? Click each axis to select the title of your list for each one. Example 1: What polynomial function has a graph that passes through the four points (0,-3), (1,-1),(2,5), and (-1,-7)? 4: Analyze 6: Regression 5: Show Cubic Example 1: What polynomial function has a graph that passes through the four points (0,-3), (1,-1),(2,5), and (-1,-7)? Click each axis to select the title of your list for each one. Example 1: What polynomial function has a graph that passes through the four points (0,-3), (1,-1),(2,5), and (-1,-7)? 4: Analyze 6: Regression 5: Show Cubic 4 2/11/2014 Which of the two graphs below do you think accurately describes the realworld situation? Extrapolation and Interpolation Interpolation: Estimating within the given domain (usually using an equation). Extrapolation: Estimating outside the given domain (using an equation). Interpolation is more reliable. Extrapolation becomes less and less reliable the farther you move from the data. Use year 0 for 1900! 5 2/11/2014 Questions on homework ? We would have the least amount of confidence in 2012 because it is not within our original data. HW: Pg. 335 #10,12,14,16-23, 28, 33, 36 6