5-1 Modeling Data With Quadratic Functions. Quadratic Function A function that can be written in the standard form: Where a ≠ 0.

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Presentation transcript:

5-1 Modeling Data With Quadratic Functions

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

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

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

Check Understanding #1 A – C p. 235

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.

Below is the graph of y = x 2 – 6x 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.

Check understanding P. 235 # 2 A and B

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

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

Check Understanding #3

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) Wave Speed (m/s)

(continued) Wavelength (m) Wave Speed (m/s) 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 x – At a wavelength of 6 meters the wave speed is approximately 23m/s.

Homework P # 1 – 37 EOO