ALGEBRA 25.8: Curve Fitting With Quadratic Models

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 = Linear2nd differences are constant = Quadratic

1 2 3 4 5

-2 0 2 4 6

0 1 2 3 4

1 2 5 10 17

Ex 1: Determine whether each data set could represent a quadratic function. Explain

A)B)

x 1 3 5 7 9

y -1 1 7 17 31

x 3 4 5 6 7

y 1 3 9 27 81

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)

Short way to set up the matrices.

Ex 2: Find a quadratic equation that fits the points (1, -5) (3, 5) and (4, 16)

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

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

Assignment #8 page 377 #’s 12-19,(58)