1. 5-1 Modeling Data With Quadratic Functions

2. Quadratic Function A function that can be written in the standard form: Where a ≠ 0

3. Determine whether each function is linear or quadratic. Identify the quadratic, linear and constant terms Ex. 1A: = (2x – 1)(2x – 1 ) Multiply Quadratic term = Linear term =-4x Constant term =1

4. Ex. 1B = 1 Quadratic term = Linear term = Constant term = none 0x or 0 1

5. Check Understanding #1 A – C p. 235

6. Graph of Quadratic Function The graph of a quadratic function is a parabola. The axis of symmetry is the line that divides a parabola into two equal parts that are mirror images. The vertex of a parabola is the point at which the parabola intersects the axis of symmetry.

7. Below is the graph of y = x 2 – 6x + 11. Identify the vertex and the axis of symmetry. Identify points corresponding to P and Q. 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.

8. Check understanding P. 235 # 2 A and B

9. Ex. 3: Find a quadratic function to model the values in the table. xyxy –2 –17 1 10 5 –10 Substitute the values of x and y into Solve the system for a, b and c.

10. Ex. 3 continued Use augmented matrices and the rref function to solve. A= -2, b = 7, c = 5

11. Check Understanding #3

12. 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

13. (continued) 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). An approximate model of the quadratic function is y = 0.59x 2 + 0.34x – 0.33. At a wavelength of 6 meters the wave speed is approximately 23m/s.

14. Homework P. 237. # 1 – 37 EOO