5.7 – Curve Fitting with Quadratic Models

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Presentation transcript:

5.7 – Curve Fitting with Quadratic Models Objectives: Find a quadratic function that exactly fits three data points. Find a quadratic model to represent a data set. Standard: 2.8.11.A. Analyze a given set of data for the existence of a pattern and represent it graphically.

Fitting a set of data with a quadratic model is an example of curve fitting.

Ex 2. Find a quadratic function whose graph contains the points (4, 3), (2, -3), and (6, 1). Quadratic Equation Simplified (4, 3) a(4)2 + b(4) + c = 3 16a + 4b + c = 3 (2, -3) a(2)2 + b(2) + c = -3 4a + 2b + c = -3 (6, 1) a(6)2 + b(6) + c = 1 36a + 6b + c = 1

Find A-1B, to solve for a, b and c. Therefore, y = -x2 + 9x – 17.

Example 2 Make a scatter plot of the data below. Find the quadratic model to represent this data. y = 0.008x2 + 0.518x + 131.886 x y 25 150 50 178 75 216 100 265 125 323 392 175 470.4