1. 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:
A. Analyze a given set of data for the existence of a pattern and represent it graphically.

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

4. 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

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

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