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Modeling quadratic fxns
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3. Below is the graph of y = x 2 – 6 x + 11. Identify the vertex and the axis of symmetry. Identify points corresponding to P and Q . Modeling Data With Quadratic Functions LESSON 5-1 Additional Examples The vertex is (3, 2). The axis of symmetry is x = 3. P (1, 6) is two units to the left of the axis of symmetry. Corresponding point P (5, 6) is two units to the right of the axis of symmetry. Q (4, 3) is one unit to the right of the axis of symmetry. Corresponding point Q (2, 3) is one unit to the left of the axis of symmetry.
4. Find the quadratic function to model the values in the table. The solution is a = –2, b = 7, c = 5. Substitute these values into standard form. The quadratic function is y = –2 x 2 + 7 x + 5. Using one of the methods of Chapter 3, solve the system Modeling Data With Quadratic Functions LESSON 5-1 Additional Examples x y – 2 – 17 1 10 5 – 10 Substitute the values of x and y into y = ax 2 + bx + c . The result is a system of three linear equations. y = ax 2 + bx + c 4 a – 2 b + c = –17 a + b + c = 10 25 a + 5 b + c = –10 { – 17 = a (–2) 2 + b (–2) + c = 4 a – 2 b + c Use (–2, –17). 10 = a (1) 2 + b (1) + c = a + b + c Use (1, 10). – 10 = a (5) 2 + b (5) + c = 25 a + 5 b + c Use (5, –10).
5. The table shows data about the wavelength x (in meters) and the wave speed y (in meters per second) of deep water ocean waves. Use the graphing calculator to model the data with a quadratic function. Graph the data and the function. Use the model to estimate the wave speed of a deep water wave that has a wavelength of 6 meters. Wavelength (m) 3 5 7 8 Wave Speed (m/s) 6 16 31 40 Modeling Data With Quadratic Functions LESSON 5-1 Additional Examples
6. (continued) An approximate model of the quadratic function is y = 0.59 x 2 + 0.34 x – 0.33. At a wavelength of 6 meters the wave speed is approximately 23m/s. Modeling Data With Quadratic Functions LESSON 5-1 Additional Examples Wavelength (m) 3 5 7 8 Wave Speed (m/s) 6 16 31 40 Step 1: Enter the data. Use QuadReg. Step 2: Graph the data and the function. Step 3: Use the table feature to find ƒ (6).
![Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. a. ƒ ( x ) = (2 x – 1) 2 This is a quadratic function. Quadratic term: 4 x 2 Linear term: –4 x Constant term: 1 Modeling Data With Quadratic Functions LESSON 5-1 Additional Examples = (2 x – 1)(2 x – 1) Multiply. ,[object Object],Write in standard form.](https://image.slidesharecdn.com/modelingquadraticfxns-110303185449-phpapp01/85/modeling-quadratic-fxns-1-320.jpg)
![(continued) b. ƒ ( x ) = x 2 – ( x + 1)( x – 1) This is a linear function. Quadratic term: none Linear term: 0 x (or 0) Constant term: 1 Modeling Data With Quadratic Functions LESSON 5-1 Additional Examples = x 2 – ( x 2 – 1) Multiply. ,[object Object],Write in standard form.](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)