1. ALGEBRA 2 5.8: Curve Fitting With Quadratic Models

2. Finite Differences
When you have a set of data that has the x’s equally spaced, you can use finite differences to find out what type of equation would best fit it.
1st differences are constant = Linear
2nd differences are constant = Quadratic 1 2 3 4 5 -2 6 1 2 3 4 5 10 17

3. Ex 1: Determine whether each data set could represent a quadratic function. Explain
A) B) x 1 3 5 7 9 y -1 17 31 x 3 4 5 6 7 y 1 9 27 81

4. Use Matrices to Write a Quadratic Function
Need 3 points
Use ax2 + bx + c = y to plug in x’s and y’s
Use inverse or augmented matrices and calculator to solve for a, b, and c
(1,-1)
(3, 1)
(5, 7)

5. Short way to set up the matrices.
Ex 2: Find a quadratic equation that fits the points (1, -5) (3, 5) and (4, 16)

6. Quadratic Regression
Can use the calculator to estimate a quadratic equation through a set of data
Steps
Enter data in lists (stat, edit)
Make sure diagnostic is on (catalog)
Run a quadratic regression (stat, calc, QuadReg)
You can plot data and graph equation to see how it fits
r tells you how well it fits the data

7. Ex 3: The table shows the cost of circular plastic wading pools based on the pools’ diameter. Find a quadratic model for the cost of a pool, given its diameter. Use the model to estimate the cost of a pool with a diameter of 8 ft.
Diameter (ft)
Cost 4
$19.95 5
$20.25 6
$25.00 7
$34.95

8. Assignment #8 page 377 #’s 12-19,(58)